Answers (Lesson 3-1) - Merrimack High School...Lesson 3-1 Write Equations Writing equations is one...
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© Glencoe/McGraw-Hill A2 Glencoe Algebra 1 Study Guide and Intervention Writing Equations NAME ______________________________________________ DATE ____________ PERIOD _____ 3-1 3-1 © Glencoe/McGraw-Hill 137 Glencoe Algebra 1 Lesson 3-1 Write Equations Writing equations is one strategy for solving problems. You can use a variable to represent an unspecified number or measure referred to in a problem. Then you can write a verbal expression as an algebraic expression. Translate each sentence into an equation or a formula. a. Ten times a number x is equal to 2.8 times the difference y minus z. 10 x = 2.8 ( y - z) The equation is 10x = 2.8( y - z). b. A number m minus 8 is the same as a number n divided by 2. m - 8 = n 2 The equation is m - 8 = . c. The area of a rectangle equals the length times the width. Translate this sentence into a formula. Let A = area, = length, and w = width. Formula: Area equals length times width. A = w The formula for the area of a rectangle is A = w. n 2 Use the Four-Step Problem-Solving Plan. The population of the United States in 2001 was about 284,000,000, and the land area of the United States is about 3,500,000 square miles. Find the average number of people per square mile in the United States. Source: www.census.gov Step 1 Explore You know that there are 284,000,000 people. You want to know the number of people per square mile. Step 2 Plan Write an equation to represent the situation. Let p represent the number of people per square mile. 3,500,000 p = 284,000,000 Step 3 Solve 3,500,000 p = 284,000,000. 3,500,000p = 284,000,000 Divide each side by p 81.14 3,500,000. There about 81 people per square mile. Step 4 Examine If there are 81 people per square mile and there are 3,500,000 square miles, 81 3,500,000 = 283,500,000, or about 284,000,000 people. The answer makes sense. Example 1 Example 1 Example 2 Example 2 Exercises Exercises Translate each sentence into an equation or formula. 1. Three times a number t minus twelve equals forty. 3t - 12 = 40 2. One-half of the difference of a and b is 54. (a - b) = 54 3. Three times the sum of d and 4 is 32. 3(d + 4) = 32 4. The area A of a circle is the product of and the radius r squared. A =r 2 WEIGHT LOSS For Exercises 5–6, use the following information. Lou wants to lose weight to audition for a part in a play. He weighs 160 pounds now. He wants to weigh 150 pounds. 5. If p represents the number of pounds he wants to lose, write an equation to represent this situation. 160 - p = 150 6. How many pounds does he need to lose to reach his goal? 10 lb 1 2 © Glencoe/McGraw-Hill 138 Glencoe Algebra 1 Write Verbal Sentences You can translate equations into verbal sentences. Translate each equation into a verbal sentence. a. 4n - 8 = 12. 4n - 8 = 12 Four times n minus eight equals twelve. b. a 2 + b 2 = c 2 a 2 + b 2 = c 2 The sum of the squares of a and b is equal to the square of c. Translate each equation into a verbal sentence. 1. 4a - 5 = 23 2. 10 + k = 4k 4 times a minus 5 is equal to 23. The sum of 10 and k is equal to 4 times k. 3. 6xy = 24 4. x 2 + y 2 = 8 6 times the product of x and y is The sum of the squares of x and equal to 24. y is equal to 8. 5. p + 3 = 2p 6. b = (h - 1) The sum of p and 3 is equal to b is of the difference of h and 1. 2 times p. 7. 100 - 2x = 80 8. 3(g + h) = 12 100 minus 2 times x is equal 3 times the sum of g and h is 12. to 80. 9. p 2 - 2p = 9 10. C = (F - 32) The square of p minus 2 times C is equal to of the difference of p is equal to 9. F and 32. 11. V = Bh 12. A = hb V is equal to of the product of A is equal to of the product of B and h. h and b. 1 2 1 3 1 2 1 3 5 9 5 9 1 3 1 3 Study Guide and Intervention (continued) Writing Equations NAME ______________________________________________ DATE ____________ PERIOD _____ 3-1 3-1 Example Example Exercises Exercises Answers (Lesson 3-1)
Transcript of Answers (Lesson 3-1) - Merrimack High School...Lesson 3-1 Write Equations Writing equations is one...
© Glencoe/McGraw-Hill A2 Glencoe Algebra 1
Stu
dy G
uid
e a
nd I
nte
rven
tion
Wri
tin
g E
qu
ati
on
s
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-1
3-1
©G
lencoe/M
cG
raw
-Hill
137
Gle
ncoe A
lgebra
1
Lesson 3-1
Wri
te E
qu
ati
on
sW
riti
ng e
qu
ati
ons
is o
ne
stra
tegy f
or s
olvin
g p
roble
ms.
You
can
use
avari
able
to
rep
rese
nt
an
un
spec
ifie
d n
um
ber
or
mea
sure
ref
erre
d t
o in
a p
roble
m.T
hen
you
can
wri
te a
ver
bal
exp
ress
ion
as
an
alg
ebra
ic e
xp
ress
ion
.
Tra
nsl
ate
ea
ch
sen
ten
ce i
nto
an
eq
ua
tio
n o
r a
form
ula
.
a.
Ten
tim
es
a n
um
ber x
is
eq
ua
l to
2.8
tim
es
the d
iffe
ren
ce y
min
us
z.
10 3
x5
2.8
3(y
2z)
Th
e eq
uati
on i
s 10x
52.8
(y2
z).
b.
A n
um
ber m
min
us
8 i
s th
e s
am
ea
s a
nu
mb
er n
div
ided
by
2.
m2
8 5
n4
2T
he
equ
ati
on i
s m
28 5
.
c.
Th
e a
rea
of
a r
ecta
ng
le e
qu
als
th
ele
ng
th t
imes
the w
idth
.T
ra
nsl
ate
this
sen
ten
ce i
nto
a f
orm
ula
.
Let
A5
are
a,
,5
len
gth
,an
d
w5
wid
th.
For
mu
la:A
rea
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als
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gth
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es
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th.
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w
Th
e fo
rmu
la f
or t
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gle
is
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.
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Use
th
e F
ou
r-S
tep
P
ro
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tes
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ple
per s
qu
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ile i
n t
he U
nit
ed
Sta
tes.
Sourc
e:
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s.gov
Ste
p 1
Exp
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You
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Pla
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Exa
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Th
e an
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mak
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ense
.
Example
1Example
1Example
2Example
2
Exercises
Exercises
Tra
nsl
ate
ea
ch
sen
ten
ce i
nto
an
eq
ua
tio
n o
r f
orm
ula
.
1.
Th
ree
tim
es a
nu
mber
tm
inu
s tw
elve
equ
als
for
ty.
3t
212 5
40
2.
On
e-h
alf
of
the
dif
fere
nce
of
aan
d b
is 5
4.
(a2
b)
554
3.
Th
ree
tim
es t
he
sum
of
dan
d 4
is
32.
3(d
14)
532
4.
Th
e are
a A
of a
cir
cle
is t
he
pro
du
ct o
f p
an
d t
he
rad
ius
rsq
uare
d.
A5
pr
2
WE
IGH
T L
OS
SF
or E
xercis
es
5–6,
use
th
e f
oll
ow
ing
in
form
ati
on
.
Lou
wan
ts t
o lo
se w
eigh
t to
au
dit
ion
for
a p
art
in
a p
lay.
He
wei
gh
s 160 p
oun
ds
now
.H
ew
an
ts t
o w
eigh
150 p
oun
ds.
5.
If p
rep
rese
nts
th
e n
um
ber
of
pou
nd
s h
e w
an
ts t
o lo
se,w
rite
an
equ
ati
on t
o re
pre
sen
tth
is s
itu
ati
on.
160 2
p5
150
6.
How
man
y p
oun
ds
doe
s h
e n
eed
to
lose
to
reach
his
goa
l?10 l
b
1 } 2
©G
lencoe/M
cG
raw
-Hill
138
Gle
ncoe A
lgebra
1
Wri
te V
erb
al
Sen
ten
ces
You
can
tra
nsl
ate
equ
ati
ons
into
ver
bal
sen
ten
ces.
Tra
nsl
ate
ea
ch
eq
ua
tio
n i
nto
a v
erb
al
sen
ten
ce.
a.
4n
28 5
12.
4n
28
512
Fou
r ti
mes
nm
inu
s ei
gh
t eq
uals
tw
elve.
b.
a2
1b
25
c2
a2
1b
25
c2
Th
e su
m o
f th
e sq
uare
s of
aan
d b
is
equ
al
to t
he
squ
are
of
c.
Tra
nsl
ate
ea
ch
eq
ua
tio
n i
nto
a v
erb
al
sen
ten
ce.
1.
4a
25 5
23
2.
10 1
k5
4k
4 t
imes a
min
us 5
is e
qu
al
to 2
3.
Th
e s
um
of
10 a
nd
kis
eq
ual
to
4ti
mes k
.
3.
6xy
524
4.
x2
1y
25
8
6 t
imes t
he p
rod
uct
of
xan
d y
is
Th
e s
um
of
the s
qu
are
s o
f x
an
d
eq
ual
to 2
4.
y i
s e
qu
al
to 8
.
5.
p1
3 5
2p
6.
b5
(h2
1)
Th
e s
um
of
pan
d 3
is e
qu
al
to
bis
o
f th
e d
iffe
ren
ce o
f h
an
d 1
.2 t
imes p
.
7.
100 2
2x
580
8.
3(g
1h
) 5
12
100 m
inu
s 2
tim
es x
is e
qu
al
3 t
imes t
he s
um
of
gan
d h
is 1
2.
to 8
0.
9.
p2
22
p5
910.
C5
(F2
32)
Th
e s
qu
are
of
pm
inu
s 2
tim
es
Cis
eq
ual
to
of
the d
iffe
ren
ce o
fp
is e
qu
al
to 9
.F
an
d 3
2.
11.V
5B
h12.
A5
hb
Vis
eq
ual
to
of
the p
rod
uct
of
Ais
eq
ual
to
of
the p
rod
uct
of
Ban
d h
.h
an
d b
.
1 } 21 } 3
1 } 2
1 } 3
5 } 9
5 } 91 } 31 } 3
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued)
Wri
tin
g E
qu
ati
on
s
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-1
3-1 Example
Example
Exercises
Exercises
Answers (Lesson 3-1)
© Glencoe/McGraw-Hill A3 Glencoe Algebra 1
An
swers
Skil
ls P
racti
ce
Wri
tin
g E
qu
ati
on
s
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-1
3-1
©G
lencoe/M
cG
raw
-Hill
139
Gle
ncoe A
lgebra
1
Lesson 3-1
Tra
nsl
ate
ea
ch
sen
ten
ce i
nto
an
eq
ua
tio
n.
1.
Tw
o ad
ded
to
thre
e ti
mes
a n
um
ber
mis
th
e sa
me
as
18.
3m
12 5
18
2.
Tw
ice
ain
crea
sed
by t
he
cube
of a
equ
als
b.
2a
1a
35
b
3.
Sev
en l
ess
than
th
e su
m o
f p
an
d q
is a
s m
uch
as
6.
(p 1
q)
27 5
6
4.
Th
e su
m o
f x
an
d i
ts s
qu
are
is
equ
al
to y
tim
es z
.x 1
x2
5yz
5.
Fou
r ti
mes
th
e su
m o
f f
an
d g
is i
den
tica
l to
six
tim
es g
.4
(f1
g)
56g
Tra
nsl
ate
ea
ch
sen
ten
ce i
nto
a f
orm
ula
.
6.
Th
e p
erim
eter
Pof
a s
qu
are
equ
als
fou
r ti
mes
th
e le
ngth
of
a s
ide
s.P
54s
7.
Th
e are
a A
of a
squ
are
is
the
len
gth
of
a s
ide
ssq
uare
d.
A5
s2
8.
Th
e p
erim
eter
Pof
a t
rian
gle
is
equ
al
to t
he
sum
of
the
len
gth
s of
sid
es a
,b,an
d c
.P
5a
1b
1c
9.
Th
e are
a A
of a
cir
cle
is p
i ti
mes
th
e ra
diu
s r
squ
are
d.
A5
pr
2
10.T
he
vol
um
e V
of a
rec
tan
gu
lar
pri
sm e
qu
als
th
e p
rod
uct
of
the
len
gth
,,
the
wid
th w
,an
d t
he
hei
gh
t h
.V
5,w
h
Tra
nsl
ate
ea
ch
eq
ua
tio
n i
nto
a v
erb
al
sen
ten
ce.
11.g 1
10 5
3g
12.
2p
14q
520
gp
lus 1
0 i
s t
he s
am
e a
sTw
ice p
plu
s 4
tim
es q
is 2
0.
3 t
imes g
.
13.4(a
1b)
59a
14.
8 2
6x
54 1
2x
4 t
imes t
he s
um
of
aan
d b
8 m
inu
s 6
tim
es x
is 4
plu
s
is 9
tim
es a
.2 t
imes x
.
15.
(f1
y)
5f
25
16.
s22
n2
52b
Half
of
the s
um
of
fan
d y
is
ssq
uare
d m
inu
s n
sq
uare
d i
s
fm
inu
s 5
.tw
ice b
.
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e a
pro
ble
m b
ase
d o
n t
he g
iven
in
form
ati
on
.
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st p
er p
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f p
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fee
bea
ns
18.
p5
cost
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ner
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cost
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pou
nd
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flavor
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offe
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ns
0.1
5p
5co
st o
f a 1
5%
tip
2c
1(c
13)
521
p1
0.1
5p
523
Sam
ple
an
sw
er:
Th
e c
ost
of
two
po
un
ds
Sam
ple
an
sw
er:
Th
e c
ost
of
of
pla
in c
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s $
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ow
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ow
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ch
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1 p
ou
nd
of
pla
in b
ean
s c
ost?
din
ner?
1 } 2
©G
lencoe/M
cG
raw
-Hill
140
Gle
ncoe A
lgebra
1
Tra
nsl
ate
ea
ch
sen
ten
ce i
nto
an
eq
ua
tio
n.
1.
Fif
ty-t
hre
e p
lus
fou
r ti
mes
cis
as
mu
ch a
s 21.
53 1
4c
521
2.
Th
e su
m o
f fi
ve
tim
es h
an
d t
wic
e g
is e
qu
al
to 2
3.
5h
12g
523
3.
On
e fo
urt
h t
he
sum
of
ran
d t
en i
s id
enti
cal
to r
min
us
4.
(r1
10)
5r
24
4.
Th
ree
plu
s th
e su
m o
f th
e sq
uare
s of
wan
d x
is 3
2.
3 1
(w2
1x
2)
532
Tra
nsl
ate
ea
ch
sen
ten
ce i
nto
a f
orm
ula
.
5.
Deg
rees
Kel
vin
Keq
uals
273 p
lus
deg
rees
Cel
siu
s C
.K
5273 1
C
6.
Th
e to
tal
cost
Cof
gas
is t
he
pri
ce p
per
gall
on t
imes
th
e n
um
ber
of
gall
ons
g.
C5
pg
7.
Th
e su
m S
of
the
mea
sure
s of
th
e an
gle
s of
a p
olygon
is
equ
al
to 1
80 t
imes
th
e d
iffe
ren
ceof
th
e n
um
ber
of
sid
es n
an
d 2
.S
5180(n
22)
Tra
nsl
ate
ea
ch
eq
ua
tio
n i
nto
a v
erb
al
sen
ten
ce.
8.
q2
(4 1
p)
5q
qm
inu
s t
he s
um
9.
t1
2 5
t
of
4 a
nd
p e
qu
als
ti
mes q
.Tw
o m
ore
th
an
o
f t
eq
uals
t.
10.9(y
21
x)
518
9 t
imes t
he s
um
11.
2(m
2n
) 5
v1
7Tw
ice t
he q
uan
tity
of
ysq
uare
d a
nd
xis
18.
mm
inu
s n
is v
plu
s 7
.
Writ
e a
pro
ble
m b
ase
d o
n t
he g
iven
in
form
ati
on
.
12.a
5co
st o
f on
e ad
ult
’s t
ick
et t
o zo
o13.
c5
regu
lar
cost
of
one
air
lin
e ti
cket
a2
4 5
cost
of
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dre
n’s
tic
ket
to
zoo
0.2
0c
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oun
t of
20%
pro
mot
ion
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dis
cou
nt
2a
14(a
24)
538
3(c
20.2
0c)
5330
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ple
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er:
Th
e c
ost
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two
S
am
ple
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Th
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ost
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ult
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ickets
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d 4
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ren
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lin
e t
ickets
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at
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dis
co
un
ted
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ckets
to
th
e z
oo
is $
38.H
ow
20%
is $
330.W
hat
is t
he r
eg
ula
r m
uch
is a
n a
du
lt’s
tic
ket?
co
st
of
a t
icket?
14.G
EO
GR
AP
HY
Abou
t 15%
of
all
fed
erall
y-o
wn
ed l
an
d i
n t
he
48 c
onti
gu
ous
state
s of
th
eU
nit
ed S
tate
s is
in
Nev
ad
a.If
Fre
pre
sen
ts t
he
are
a o
f fe
der
all
y-o
wn
ed l
an
d i
n t
hes
est
ate
s,an
d N
rep
rese
nts
th
e p
orti
on i
n N
evad
a,w
rite
an
equ
ati
on f
or t
his
sit
uati
on.
0.1
5F
5N
FIT
NE
SS
Fo
r E
xercis
es
15–1
7,
use
th
e f
oll
ow
ing
in
form
ati
on
.
Dea
nn
a a
nd
Pie
tra e
ach
go
for
walk
s aro
un
d a
lak
e a f
ew t
imes
per
wee
k.L
ast
wee
k,
Dea
nn
a w
alk
ed 7
mil
es m
ore
than
Pie
tra.
15.If
pre
pre
sen
ts t
he
nu
mber
of
mil
es P
ietr
a w
alk
ed,w
rite
an
equ
ati
on t
hat
rep
rese
nts
th
eto
tal
nu
mber
of
mil
es T
the
two
gir
ls w
alk
ed.
T5
p1
(p1
7)
16.If
Pie
tra w
alk
ed 9
mil
es d
uri
ng t
he
wee
k,h
ow m
an
y m
iles
did
Dea
nn
a w
alk
?16 m
i
17.If
Pie
tra w
alk
ed 1
1 m
iles
du
rin
g t
he
wee
k,h
ow m
an
y m
iles
did
th
e tw
o gir
ls w
alk
toget
her
?29 m
i
3 } 51 } 3
3 } 5
1 } 3
1 } 4
Pra
cti
ce (
Avera
ge)
Wri
tin
g E
qu
ati
on
s
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-1
3-1
Answers (Lesson 3-1)
© Glencoe/McGraw-Hill A4 Glencoe Algebra 1
Readin
g t
o L
earn
Math
em
ati
cs
Wri
tin
g E
qu
ati
on
s
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-1
3-1
©G
lencoe/M
cG
raw
-Hill
141
Gle
ncoe A
lgebra
1
Lesson 3-1
Pre
-Act
ivit
yH
ow
are e
qu
ati
on
s u
sed
to
desc
rib
e h
eig
hts
?
Rea
d t
he
intr
odu
ctio
n t
o L
esso
n 3
-1 a
t th
e to
p o
f p
age
120 i
n y
our
textb
ook
.
Doe
s th
e eq
uati
on 3
05 2
s5
154 a
lso
rep
rese
nt
the
situ
ati
on?
Exp
lain
.
Yes;
the t
ota
l h
eig
ht
min
us t
he h
eig
ht
of
the s
tatu
e i
tself
giv
es
the h
eig
ht
of
the p
ed
esta
l.
Read
ing
th
e L
ess
on
1.
Tra
nsl
ate
each
sen
ten
ce i
nto
an
equ
ati
on.
a.
Tw
otim
es
the s
um
of
xand t
hre
em
inus
four
equals
four
tim
es
x.
23
(x1
3)
24
54
3x
b.
The d
iffe
rence o
f k
and 3
istw
otim
es
kdiv
ided b
yfive.
k2
35
23
k4
5
2.
A 1
oz
serv
ing o
f ch
ips
has
140 c
alo
ries
.T
her
e are
abou
t 14 s
ervin
gs
of c
hip
s in
a b
ag.
How
man
y c
alo
ries
are
th
ere
in a
bag o
f ch
ips?
Wri
te w
hat
you
r so
luti
on w
ould
be
as
you
use
each
ste
p i
n t
he
Fou
r-S
tep
Pro
ble
m-S
olvin
g P
lan
.
Exp
lore
Wh
at
do
you
kn
ow?
A 1
oz s
erv
ing
of
ch
ips h
as 1
40 c
alo
ries a
nd
th
ere
are
14
serv
ing
s o
f ch
ips i
n a
bag
.W
hat
do
you
wan
t to
kn
ow?
Ho
w m
an
y c
alo
ries a
re i
n a
bag
of
ch
ips?
Pla
nW
rite
an
equ
ati
on.
140 ?
14 5
x
Solv
eS
olve
the
pro
ble
m.
140 ?
14 5
1960;T
here
are
1960 c
alo
ries i
n a
bag
of
ch
ips.
Exa
min
eD
oes
you
r an
swer
mak
e se
nse
?
See s
tud
en
ts’w
ork
.
Help
ing
Yo
u R
em
em
ber
3.
If y
ou c
an
not
rem
ember
all
th
e st
eps
of t
he
Fou
r-S
tep
Pro
ble
m-S
olvin
g P
lan
,tr
y t
ore
mem
ber
th
e fi
rst
lett
ers
of t
he
firs
t w
ord
in
each
ste
p.W
rite
th
ose
lett
ers
her
e w
ith
thei
r ass
ocia
ted
wor
ds.
EP
SE
;E
xp
lore
,P
lan
,S
olv
e,E
xam
ine
©G
lencoe/M
cG
raw
-Hill
142
Gle
ncoe A
lgebra
1
Rep
-Tiles
A r
ep-t
ile
is a
fig
ure
th
at
can
be
subd
ivid
ed i
nto
sm
all
er c
opie
s of
its
elf.
Th
e la
rge
figu
re i
s si
mil
ar
to t
he
small
on
es a
nd
th
e sm
all
fig
ure
s are
all
con
gru
ent.
Sh
ow
th
at
ea
ch
fig
ure i
s a
rep
-til
e b
y s
ub
div
idin
g i
t in
to f
ou
r s
ma
ller a
nd
si
mil
ar f
igu
res.
1.
2.
3.
4.
5.
6.
Su
bd
ivid
e e
ach
rep
-til
e i
nto
nin
e s
ma
ller a
nd
sim
ila
r f
igu
res.
7.
8.
9.
10.
En
rich
men
t
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-1
3-1
Answers (Lesson 3-1)
© Glencoe/McGraw-Hill A5 Glencoe Algebra 1
An
swers
Stu
dy G
uid
e a
nd I
nte
rven
tion
So
lvin
g E
qu
ati
on
s b
y U
sin
g A
dd
itio
n a
nd
Su
btr
acti
on
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-2
3-2
©G
lencoe/M
cG
raw
-Hill
143
Gle
ncoe A
lgebra
1
Lesson 3-2
So
lve U
sin
g A
dd
itio
nIf
th
e sa
me
nu
mber
is
ad
ded
to
each
sid
e of
an
equ
ati
on,th
ere
sult
ing e
qu
ati
on i
s eq
uiv
ale
nt
to t
he
orig
inal
one.
In g
ener
al
if t
he
orig
inal
equ
ati
onin
vol
ves
su
btr
act
ion
,th
is p
rop
erty
wil
l h
elp
you
sol
ve
the
equ
ati
on.
Ad
dit
ion
Pro
pert
y o
f E
qu
ality
For
any n
um
bers
a,
b,
and c
, if a
5b,
then a
1c
5b
1c.
So
lve m
232 5
18.
m2
32 5
18
Origin
al equation
m2
32 1
32 5
18 1
32
Add 3
2 t
o e
ach s
ide.
m5
50
Sim
plif
y.
Th
e so
luti
on i
s 50.
So
lve 2
18 5
p2
12.
218 5
p2
12
Origin
al equation
218 1
12 5
p2
12 1
12
Add 1
2 t
o e
ach s
ide.
p5
26
Sim
plif
y.
Th
e so
luti
on i
s 2
6.
Example
1Example
1Example
2Example
2
Exercises
Exercises
So
lve e
ach
eq
ua
tio
n.T
hen
ch
eck
yo
ur s
olu
tio
n.
1.
h2
3 5
22
12.
m 2
8 5
212
24
3.
p2
5 5
15
20
4.
20 5
y2
828
5.
k2
0.5
52.3
2.8
6.
w2
51
7.
h2
18 5
217
18.
212 5
224 1
k12
9.
j2
0.2
51.8
2
10.b
240 5
240
011.
m2
(212)
510
22
12.
w2
5
Writ
e a
n e
qu
ati
on
fo
r e
ach
pro
ble
m.T
hen
so
lve t
he e
qu
ati
on
an
d c
heck
th
eso
luti
on
.
13.T
wel
ve
subtr
act
ed f
rom
a n
um
ber
equ
als
25.F
ind
th
e n
um
ber
.n
212 5
25;
37
14.W
hat
nu
mber
dec
rease
d b
y 5
2 e
qu
als
212?
n2
52 5
212;
40
15.F
ifty
su
btr
act
ed f
rom
a n
um
ber
equ
als
eig
hty
.F
ind
th
e n
um
ber
.n
250 5
80;
130
16.W
hat
nu
mber
min
us
one-
half
is
equ
al
to n
egati
ve
one-
half
?n
2
52
;0
17.T
he
dif
fere
nce
of
a n
um
ber
an
d e
igh
t is
equ
al
to 1
4.W
hat
is t
he
nu
mber
?
n2
8 5
14;
22
18.A
nu
mber
dec
rease
d b
y f
ourt
een
is
equ
al
to e
igh
teen
.W
hat
is t
he
nu
mber
?
n2
14 5
18;
32
1 } 21 } 2
7 } 41 } 4
3 } 2
1 } 85 } 8
1 } 2
©G
lencoe/M
cG
raw
-Hill
144
Gle
ncoe A
lgebra
1
So
lve U
sin
g S
ub
tract
ion
If t
he
sam
e n
um
ber
is
subtr
act
ed f
rom
each
sid
e of
an
equ
ati
on,th
e re
sult
ing e
qu
ati
on i
s eq
uiv
ale
nt
to t
he
orig
inal
one.
In g
ener
al
if t
he
orig
inal
equ
ati
on i
nvol
ves
ad
dit
ion
,th
is p
rop
erty
wil
l h
elp
you
sol
ve
the
equ
ati
on.
Su
btr
acti
on
Pro
pert
y o
f E
qu
ality
For
any n
um
bers
a,
b,
and c
, if a
5b,
then a
2c
5b
2c.
So
lve 2
2 1
p5
212.
22 1
p5
212
Origin
al equation
22 1
p2
22 5
212 2
22
Subtr
act
22 f
rom
each s
ide.
p5
234
Sim
plif
y.
Th
e so
luti
on i
s 2
34.
So
lve e
ach
eq
ua
tio
n.T
hen
ch
eck
yo
ur s
olu
tio
n.
1.
x1
12 5
62
62.
z1
2 5
213
215
3.
217 5
b1
42
21
4.
s1
(29)
57
16
5.
23.2
5,
1(2
0.2
)2
36.
21
x5
1
7.
19 1
h5
24
223
8.
212 5
k1
24
236
9.
j1
1.2
52.8
1.6
10.b
180 5
280
2160
11.
m1
(28)
52
10
12.
w1
52
Writ
e a
n e
qu
ati
on
fo
r e
ach
pro
ble
m.T
hen
so
lve t
he e
qu
ati
on
an
d c
heck
th
eso
luti
on
.
13.T
wel
ve
ad
ded
to
a n
um
ber
equ
als
18.F
ind
th
e n
um
ber
.n
112 5
18;
6
14.W
hat
nu
mber
in
crea
sed
by 2
0 e
qu
als
210?
n1
20 5
210;
230
15.T
he
sum
of
a n
um
ber
an
d f
ifty
equ
als
eig
hty
.F
ind
th
e n
um
ber
.n
150 5
80;
30
16.W
hat
nu
mber
plu
s on
e-h
alf
is
equ
al
to f
our?
n1
54;
3
17.T
he
sum
of
a n
um
ber
an
d 3
is
equ
al
to 2
15.W
hat
is t
he
nu
mber
?n
13 5
215;
218
1 } 21 } 2
7 } 85 } 8
3 } 2
5 } 8
3 } 8
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued)
So
lvin
g E
qu
ati
on
s b
y U
sin
g A
dd
itio
n a
nd
Su
btr
acti
on
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-2
3-2 Example
Example
Exercises
Exercises
Answers (Lesson 3-2)
© Glencoe/McGraw-Hill A6 Glencoe Algebra 1
Skil
ls P
racti
ce
So
lvin
g E
qu
ati
on
s b
y U
sin
g A
dd
itio
n a
nd
Su
btr
acti
on
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-2
3-2
©G
lencoe/M
cG
raw
-Hill
145
Gle
ncoe A
lgebra
1
Lesson 3-2
So
lve e
ach
eq
ua
tio
n.T
hen
ch
eck
yo
ur s
olu
tio
n.
1.
y2
7 5
815
2.
w1
14 5
28
222
3.
p2
4 5
610
4.
213 5
5 1
x2
18
5.
98 5
b1
34
64
6.
y2
32 5
21
31
7.
s1
(228)
50
28
8.
y1
(210)
56
16
9.
21 5
s1
(219)
18
10.
j2
(217)
536
19
11.14 5
d1
(210)
24
12.
u1
(25)
52
15
210
13.11 5
216 1
y27
14.
c2
(23)
5100
97
15.47 5
w2
(28)
39
16.
x2
(274)
52
22
296
17.4 2
(2h
) 5
68
64
18.
256 5
20 2
(2e)
276
Writ
e a
n e
qu
ati
on
fo
r e
ach
pro
ble
m.T
hen
so
lve t
he e
qu
ati
on
an
d c
heck
yo
ur
solu
tio
n.
19.A
nu
mber
dec
rease
d b
y 1
4 i
s 2
46.F
ind
th
e n
um
ber
.n
214 5
246;
232
20.T
hir
teen
su
btr
act
ed f
rom
a n
um
ber
is
25.F
ind
th
e n
um
ber
.n
213 5
25;
8
21.T
he
sum
of
a n
um
ber
an
d 6
7 i
s eq
ual
to 2
34.F
ind
th
e n
um
ber
.n
167 5
234;
2101
22.W
hat
nu
mber
min
us
28 e
qu
als
22?
n2
28 5
22;
26
23.A
nu
mber
plu
s 2
73 i
s eq
ual
to 2
7.W
hat
is t
he
nu
mber
?n
1(2
73)
527;
100
24.A
nu
mber
plu
s 2
17 e
qu
als
21.F
ind
th
e n
um
ber
.n
1(2
17)
52
1;
16
25.W
hat
nu
mber
les
s 5 i
s eq
ual
to 2
39?
n2
5 5
239;
234
©G
lencoe/M
cG
raw
-Hill
146
Gle
ncoe A
lgebra
1
So
lve e
ach
eq
ua
tio
n.T
hen
ch
eck
yo
ur s
olu
tio
n.
1.
d2
8 5
17
25
2.
v1
12 5
25
217
3.
b2
2 5
211
29
4.
216 5
s1
71
287
5.
29 5
a2
76
105
6.
214 1
y5
22
12
7.
8 2
(2c)
51
27
8.
78 1
r5
215
293
9.
f1
(23)
52
92
6
10.4.2
5n
17.3
23.1
11.
w1
1.9
52
2.5
24.4
12.
4.6
2(2
b)
52
0.4
25
13.y
2(2
1.5
) 5
0.5
21
14.
a2
0.1
3 5
20.5
82
0.4
515.
k1
(24.2
1)
52
192
14.7
9
16.r
15
17.
1q
518.
5h
12
19.
1x
52
220.
y1
52
21.
22
(2n
) 5
2
Writ
e a
n e
qu
ati
on
fo
r e
ach
pro
ble
m.T
hen
so
lve t
he e
qu
ati
on
an
d c
heck
yo
ur
solu
tio
n.
22.W
hat
nu
mber
min
us
9 i
s eq
ual
to 2
18?
n2
9 5
218;
29
23.A
nu
mber
plu
s 15 e
qu
als
212.W
hat
is t
he
nu
mber
?n
115 5
212;
227
24.T
he
sum
of
a n
um
ber
an
d 2
3 i
s eq
ual
to 2
91.F
ind
th
e n
um
ber
.n
1(2
3)
52
91;
288
25.N
egati
ve
seven
teen
equ
als
63 p
lus
a n
um
ber
.W
hat
is t
he
nu
mber
?2
17 5
63 1
n;
280
26.T
he
sum
of
neg
ati
ve
14,a n
um
ber
,an
d 6
is
25.W
hat
is t
he
nu
mber
?2
14 1
n1
6 5
25;
3
27.W
hat
nu
mber
plu
s on
e h
alf
is
equ
al
to t
hre
e ei
gh
ths?
n1
5;
2
HIS
TO
RY
Fo
r E
xercis
es
28 a
nd
29,
use
th
e f
oll
ow
ing
in
form
ati
on
.
Gali
leo
Gali
lei
was
bor
n i
n 1
564.M
an
y y
ears
late
r,in
1642,S
ir I
saac
New
ton
was
bor
n.
28.W
rite
an
ad
dit
ion
equ
ati
on t
o re
pre
sen
t th
e si
tuati
on.
1564 1
y5
1642
29.H
ow m
an
y y
ears
aft
er G
ali
leo
was
bor
n w
as
Isaac
New
ton
bor
n?
78
HU
RR
ICA
NE
SF
or E
xercis
es
30 a
nd
31,
use
th
e f
oll
ow
ing
in
form
ati
on
.
Th
e d
ay a
fter
a h
urr
ican
e,th
e baro
met
ric
pre
ssu
re i
n a
coa
stal
tow
n h
as
rise
n t
o 29.7
in
ches
of
mer
cury
,w
hic
h i
s 2.9
in
ches
of
mer
cury
hig
her
th
an
th
e p
ress
ure
wh
en t
he
eye
of t
he
hu
rric
an
e p
ass
ed o
ver
.
30.W
rite
an
ad
dit
ion
equ
ati
on t
o re
pre
sen
t th
e si
tuati
on.
b1
2.9
529.7
31.W
hat
was
the
baro
met
ric
pre
ssu
re w
hen
th
e ey
e p
ass
ed o
ver
?26.8
in
.o
f m
erc
ury
1 } 83 } 8
1 } 2
7} 2
47
} 12
7 } 81
} 20
3 } 4
4 } 55 } 6
7} 1
2
1 } 4
1} 1
52 } 5
1 } 31 } 9
2 } 3
5 } 97
} 10
9} 1
0
1 } 5
Pra
cti
ce (
Avera
ge)
So
lvin
g E
qu
ati
on
s b
y U
sin
g A
dd
itio
n a
nd
Su
btr
acti
on
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-2
3-2
Answers (Lesson 3-2)
© Glencoe/McGraw-Hill A7 Glencoe Algebra 1
An
swers
Readin
g t
o L
earn
Math
em
ati
cs
So
lvin
g E
qu
ati
on
s b
y U
sin
g A
dd
itio
n a
nd
Su
btr
acti
on
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-2
3-2
©G
lencoe/M
cG
raw
-Hill
147
Gle
ncoe A
lgebra
1
Lesson 3-2
Pre
-Act
ivit
yH
ow
ca
n e
qu
ati
on
s b
e u
sed
to
co
mp
are d
ata
?
Rea
d t
he
intr
odu
ctio
n t
o L
esso
n 3
-2 a
t th
e to
p o
f p
age
128 i
n y
our
textb
ook
.
In t
he
equ
ati
on m
266 5
5,th
e n
um
ber
5 r
epre
sen
ts
the d
iffe
ren
ce b
etw
een
th
e p
erc
en
t o
f g
row
th f
or
med
ical
assis
tan
ts a
nd
th
e p
erc
en
t o
f g
row
th f
or
travel
ag
en
ts,
an
d t
he
nu
mber
66 r
epre
sen
ts
the r
ate
of
gro
wth
fo
r tr
avel
ag
en
ts.
Read
ing
th
e L
ess
on
1.
To
solv
e x
117 5
46 u
sin
g t
he
Su
btr
act
ion
Pro
per
ty o
f E
qu
ali
ty,you
wou
ld s
ubtr
act
from
each
sid
e.
2.
To
solv
e y
29 5
230 u
sin
g t
he
Ad
dit
ion
Pro
per
ty o
f E
qu
ali
ty,you
wou
ld a
dd
to e
ach
sid
e.
3.
Wri
te a
n e
qu
ati
on t
hat
you
cou
ld s
olve
by s
ubtr
act
ing 3
2 f
rom
each
sid
e.
Sam
ple
an
sw
er:
m1
32 5
50
4.
A s
tud
ent
use
d t
he
Su
btr
act
ion
Pro
per
ty o
f E
qu
ali
ty t
o so
lve
an
equ
ati
on.E
xp
lain
wh
y i
tw
ould
als
o be
pos
sible
to
use
th
e A
dd
itio
n P
rop
erty
of
Equ
ali
ty t
o so
lve
the
equ
ati
on.
Su
btr
acti
ng
on
e n
um
ber
fro
m a
no
ther
giv
es t
he s
am
e r
esu
lt a
s a
dd
ing
the o
pp
osit
e o
f th
e n
um
ber
that
was s
ub
tracte
d.
Help
ing
Yo
u R
em
em
ber
5.
Exp
lain
how
you
dec
ide
wh
eth
er t
o u
se t
he
Ad
dit
ion
Pro
per
ty o
r th
e S
ubtr
act
ion
Pro
per
ty o
f E
qu
ali
ty t
o so
lve
an
equ
ati
on.
Sam
ple
an
sw
er:
If t
he g
iven
eq
uati
on
has a
nu
mb
er
ad
ded
to
th
eva
riab
le,th
en
use t
he S
ub
tracti
on
Pro
pert
y o
f E
qu
ality
.If
th
e e
qu
ati
on
has a
nu
mb
er
su
btr
acte
d f
rom
th
e v
ari
ab
le,th
en
use t
he A
dd
itio
nP
rop
ert
y o
f E
qu
ality
.
917
©G
lencoe/M
cG
raw
-Hill
148
Gle
ncoe A
lgebra
1
Co
un
tin
g-O
ff P
uzzle
s
So
lve e
ach
pu
zzle
.
1.
Tw
enty
-fiv
e p
eop
le a
re s
tan
din
g i
n a
cir
cle.
Sta
rtin
g w
ith
per
son
1,th
ey c
oun
t of
f fr
om
1 t
o 7 a
nd
th
en s
tart
over
wit
h 1
.E
ach
p
erso
n w
ho
says
“7”
dro
ps
out
of t
he
circ
le.
Wh
o is
th
e la
st p
erso
n l
eft?
nu
mb
er
15
2.
For
ty p
eop
le s
tan
d i
n a
cir
cle.
Th
ey c
oun
t of
f so
th
at
ever
y t
hir
d
per
son
dro
ps
out.
Wh
ich
tw
o p
eop
le a
re t
he
last
on
es l
eft?
13th
an
d 2
8th
peo
ple
3.
On
ly h
alf
of
the
30 s
tud
ents
in
S
haro
n’s
cla
ss c
an
go
on a
fie
ld
trip
.S
haro
n a
rran
ges
th
e boy
s an
d g
irls
as
show
n.T
hey
cou
nt
off
from
1 t
o 9 a
nd
ever
y n
inth
per
son
dro
ps
out
un
til
only
15 p
eop
le a
re l
eft.
Wh
o get
s to
go
on t
he
fiel
d t
rip
.th
e g
irls
A g
ro
up
of
peo
ple
sta
nd
in
a c
ircle
an
d c
ou
nt
off
1,
2,
1,
2,
1 a
nd
so
on
.E
very
seco
nd
perso
n d
ro
ps
ou
t.P
erso
n n
um
ber 1
is
the
last
perso
n l
eft
.
4.
Dra
w a
dia
gra
m t
o sh
ow w
hy t
he
nu
mber
of
peo
ple
in
th
e ci
rcle
mu
st b
e ev
en.T
hen
,ex
pla
in y
our
an
swer
.If
th
e n
um
ber
is o
dd
,p
ers
on
1 w
ou
ld d
rop
ou
t aft
er
the f
irst
rou
nd
.
5.
Wh
en t
he
cou
nt
retu
rns
to p
erso
n n
um
ber
1 f
or t
he
firs
t ti
me,
how
man
y p
eop
le h
ave
dro
pp
ed o
ut?
half
of
the o
rig
inal
nu
mb
er
6.
Fin
d t
he
nu
mber
of
peo
ple
in
th
e ci
rcle
if
the
nu
mb
er i
s bet
wee
n 1
0 a
nd
20.D
o th
e sa
me
if t
he
nu
mber
is
bet
wee
n
30 a
nd
40.W
hat
can
you
con
clu
de
abou
t th
e or
igin
al
nu
mber
of
peo
ple
?16;
32;T
he n
um
ber
mu
st
be a
po
wer
of
2.
G
G
G
G
GG
GG
G
G
G
G
GG
GB
B
BB
B
B
BB
BB
B
BB
B
B
1
23
45
67
89
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
2930
12
34
5
6
7
8 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
En
rich
men
t
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-2
3-2
Answers (Lesson 3-2)
© Glencoe/McGraw-Hill A8 Glencoe Algebra 1
Stu
dy G
uid
e a
nd I
nte
rven
tion
So
lvin
g E
qu
ati
on
s b
y U
sin
g M
ult
iplicati
on
an
d D
ivis
ion
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-3
3-3
©G
lencoe/M
cG
raw
-Hill
149
Gle
ncoe A
lgebra
1
Lesson 3-3
So
lve U
sin
g M
ult
iplica
tio
nIf
each
sid
e of
an
equ
ati
on i
s m
ult
ipli
ed b
y t
he
sam
en
um
ber
,th
e re
sult
ing e
qu
ati
on i
s eq
uiv
ale
nt
to t
he
giv
en o
ne.
You
can
use
th
e p
rop
erty
to
solv
e eq
uati
ons
invol
vin
g m
ult
ipli
cati
on a
nd
div
isio
n.
Mu
ltip
licati
on
Pro
pert
y o
f E
qu
ality
For
any n
um
bers
a,
b,
and c
, if a
5b,
then a
c5
bc.
So
lve 3
p5
1.
3p
51
Origin
al equation
p5
Rew
rite
each m
ixed n
um
ber
as a
nim
pro
per
fraction.
1p25
12
Multip
ly e
ach s
ide b
y
.
p5
Sim
plif
y.
Th
e so
luti
on i
s .
3 } 7
3 } 7
2 } 7
3 } 2
2 } 7
7 } 2
2 } 7
3 } 2
7 } 2
1 } 2
1 } 2
1 } 2
1 } 2S
olv
e 2
n5
16.
2n
516
Origin
al equation
2412
n25
24(1
6)
Multip
ly e
ach s
ide b
y 2
4.
n5
264
Sim
plif
y.
Th
e so
luti
on i
s 2
64.
1 } 41 } 4
1 } 4Example
1Example
1Example
2Example
2
Exercises
Exercises
So
lve e
ach
eq
ua
tio
n.T
hen
ch
eck
yo
ur s
olu
tio
n.
1.
52
22
62.
m5
648
3.
p5
3
4.
5 5
60
5.
2k
52
2.5
10
6.
25
25
7.
21
h5
42
8.
212 5
2k
89.
51
10.
23
b5
52
111.
m5
10
14
12.
52
21
Writ
e a
n e
qu
ati
on
fo
r e
ach
pro
ble
m.T
hen
so
lve t
he e
qu
ati
on
.
13.O
ne-
fift
h o
f a n
um
ber
equ
als
25.F
ind
th
e n
um
ber
.n
525;
125
14.W
hat
nu
mber
div
ided
by 2
equ
als
218?
52
18;
236
15.A
nu
mber
div
ided
by e
igh
t eq
uals
3.F
ind
th
e n
um
ber
.5
3;
24
16.O
ne
an
d a
half
tim
es a
nu
mber
equ
als
6.F
ind
th
e n
um
ber
.1
n5
6;
41 } 2
n } 8
n } 2
1 } 5
1 } 41 } 4
p } 52 } 7
7} 1
01 } 2
1 } 3
1 } 52 } 5
j } 3
3 } 28 } 3
1 } 2
5 } 8
m } 8
1 } 4
y} 1
2
3 } 5
1 } 5
1 } 8
h } 3
©G
lencoe/M
cG
raw
-Hill
150
Gle
ncoe A
lgebra
1
So
lve U
sin
g D
ivis
ion
To
solv
e eq
uati
ons
wit
h m
ult
ipli
cati
on a
nd
div
isio
n,you
can
als
ou
se t
he
Div
isio
n P
rop
erty
of
Equ
ali
ty.If
each
sid
e of
an
equ
ati
on i
s d
ivid
ed b
y t
he
sam
en
um
ber
,th
e re
sult
ing e
qu
ati
on i
s tr
ue.
Div
isio
n P
rop
ert
y o
f E
qu
ality
For
any n
um
bers
a,
b,
and c
, w
ith c
Þ0,
if a
5b,
then
5.
b } ca } c
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued)
So
lvin
g E
qu
ati
on
s b
y U
sin
g M
ult
iplicati
on
an
d D
ivis
ion
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-3
3-3
So
lve 8
n5
64.
8n
564
Origin
al equation
5D
ivid
e e
ach s
ide b
y 8
.
n5
8S
implif
y.
Th
e so
luti
on i
s 8.
64
}8
8n
}8
So
lve 2
5n
560.
25n
560
Origin
al equation
5D
ivid
e e
ach s
ide b
y 2
5.
n5
212
Sim
plif
y.
Th
e so
luti
on i
s 2
12.
60
} 25
25n
}2
5
Example
1Example
1Example
2Example
2
Exercises
Exercises
So
lve e
ach
eq
ua
tio
n.T
hen
ch
eck
yo
ur s
olu
tio
n.
1.
3h
52
42
214
2.
8m
516
23.
23t
551
217
4.
23
r5
224
85.
8k
52
64
28
6.
22m
516
28
7.
12h
54
8.
22.4
p5
7.2
23
9.
0.5
j5
510
10.
225 5
5m
25
11.
6m
515 2
12.
21.5
p5
275
50
Writ
e a
n e
qu
ati
on
fo
r e
ach
pro
ble
m.T
hen
so
lve t
he e
qu
ati
on
.
13.F
our
tim
es a
nu
mber
equ
als
64.F
ind
th
e n
um
ber
.4n
564;
16
14.W
hat
nu
mber
mu
ltip
lied
by 2
4 e
qu
als
216?
24n
52
16;
4
15.A
nu
mber
tim
es e
igh
t eq
uals
236.F
ind
th
e n
um
ber
.8
n5
236;
24
1 } 2
1 } 2
1 } 3
Answers (Lesson 3-3)
© Glencoe/McGraw-Hill A9 Glencoe Algebra 1
An
swers
Skil
ls P
racti
ce
So
lvin
g E
qu
ati
on
s b
y U
sin
g M
ult
iplicati
on
an
d D
ivis
ion
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-3
3-3
©G
lencoe/M
cG
raw
-Hill
151
Gle
ncoe A
lgebra
1
Lesson 3-3
So
lve e
ach
eq
ua
tio
n.T
hen
ch
eck
yo
ur s
olu
tio
n.
1.
12z
5108
92.
27t
549
27
3.
18e
52
216
212
4.
222 5
11
v2
2
5.
26d
52
42
76.
96 5
224
a2
4
7.
516
64
8.
59
144
9.
284 5
2252
10.
25
213
91
11.
52
13
252
12.
31 5
2n
2186
13.
26 5
z2
914.
q5
24
214
15.
p5
210
218
16.
54
17.
20.4
b5
5.2
213
18.
1.6
m5
24
22.5
Writ
e a
n e
qu
ati
on
fo
r e
ach
pro
ble
m.T
hen
so
lve t
he e
qu
ati
on
.
19.T
he
opp
osit
e of
a n
um
ber
is
29.W
hat
is t
he
nu
mber
?2
n5
29;
9
20.F
ourt
een
tim
es a
nu
mber
is
242.F
ind
th
e n
um
ber
.14
n5
242;
23
21.E
igh
t ti
mes
a n
um
ber
equ
als
128.W
hat
is t
he
nu
mber
?8n
5128;
16
22.N
egati
ve
twel
ve
tim
es a
nu
mber
equ
als
2132.F
ind
th
e n
um
ber
.2
12
n5
2132;
11
23.N
egati
ve
eigh
teen
tim
es a
nu
mber
is
254.W
hat
is t
he
nu
mber
?2
18
n5
254;
3
24.O
ne
sixth
of
a n
um
ber
is
217.F
ind
th
e n
um
ber
.n
52
17;
2102
25.N
egati
ve
thre
e fi
fth
s of
a n
um
ber
is
215.W
hat
is t
he
nu
mber
?2
n5
215;
25
3 } 5
1 } 6
2 } 5
a} 1
0
5 } 9
2 } 7
2 } 3
1 } 6
t } 4
d } 7
d } 3
a} 1
6
c } 4
©G
lencoe/M
cG
raw
-Hill
152
Gle
ncoe A
lgebra
1
So
lve e
ach
eq
ua
tio
n.T
hen
ch
eck
yo
ur s
olu
tio
n.
1.
8j
596
12
2.
213z
52
39
33.
2180 5
15
m2
12
4.
243 5
27c
95.
52
82
72
6.
25
28
96
7.
512
8.
56
9.
54
10.
21 5
2t
11.
2w
52
924
12.
2s
54
220
13.
23x
52
14.
a5
15.
h5
16.5n
517.
2.5
k5
20
818.
23.4
e5
23.7
41.1
19.
21.7
b5
2.2
12
1.3
20.
0.2
6p
50.1
04
0.4
21.
4.2
q5
23.3
62
0.8
Writ
e a
n e
qu
ati
on
fo
r e
ach
pro
ble
m.T
hen
so
lve t
he e
qu
ati
on
.
22.N
egati
ve
nin
e ti
mes
a n
um
ber
equ
als
2117.F
ind
th
e n
um
ber
.2
9n
52
117;
13
23.N
egati
ve
one
eigh
th o
f a n
um
ber
is
2.W
hat
is t
he
nu
mber
?2
n5
2;
6
24.F
ive
sixth
s of
a n
um
ber
is
2.F
ind
th
e n
um
ber
.n
52
;2
25.2.7
tim
es a
nu
mber
equ
als
8.3
7.W
hat
is t
he
nu
mber
?2.7
n5
8.3
7;
3.1
26.O
ne
an
d o
ne
fou
rth
tim
es a
nu
mber
is
one
an
d o
ne
thir
d.W
hat
is t
he
nu
mber
?
1n
51
;1
27.P
UB
LIS
HIN
GT
wo
un
its
of m
easu
re u
sed
in
pu
bli
shin
g a
re t
he
pic
aan
d t
he
poin
t.A
pic
ais
on
e si
xth
of
an
in
ch.T
her
e are
12 p
oin
ts i
n a
pic
a,so
Poi
nts
512 ·
Pic
as.
How
man
yp
icas
are
equ
ivale
nt
to 1
08 p
oin
ts?
9 p
icas
RO
LLE
R C
OA
ST
ER
SF
or E
xercis
es
28 a
nd
29,
use
th
e f
oll
ow
ing
in
form
ati
on
.
Su
per
ma
n t
he
Esc
ap
ein
Cali
forn
ia i
s th
e fa
stes
t ro
ller
coa
ster
in
th
e w
orld
.R
ider
s fa
ll
415 f
eet
in 7
sec
ond
s.S
pee
ds
reach
a m
axim
um
of
100 m
iles
per
hou
r.
28.If
xre
pre
sen
ts t
he
aver
age
rate
of
fall
of
the
roll
er c
oast
er,w
rite
an
exp
ress
ion
to
rep
rese
nt
the
situ
ati
on (
Hin
t:U
se t
he
dis
tan
ce f
orm
ula
d5
rt.)
7x
5415
29.W
hat
is t
he
aver
age
rate
th
at
rid
ers
fall
in
fee
t p
er s
econ
d?
ab
ou
t 59.3
ft/
s
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Pra
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Avera
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So
lvin
g E
qu
ati
on
s b
y U
sin
g M
ult
iplicati
on
an
d D
ivis
ion
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-3
3-3
Answers (Lesson 3-3)
© Glencoe/McGraw-Hill A10 Glencoe Algebra 1
Readin
g t
o L
earn
Math
em
ati
cs
So
lvin
g E
qu
ati
on
s b
y U
sin
g M
ult
iplicati
on
an
d D
ivis
ion
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-3
3-3
©G
lencoe/M
cG
raw
-Hill
153
Gle
ncoe A
lgebra
1
Lesson 3-3
Pre
-Act
ivit
yH
ow
ca
n e
qu
ati
on
s b
e u
sed
to
fin
d h
ow
lo
ng
it
tak
es
lig
ht
to r
ea
ch
Ea
rth
?
Rea
d t
he
intr
odu
ctio
n t
o L
esso
n 3
-3 a
t th
e to
p o
f p
age
135 i
n y
our
textb
ook
.
•In
th
e eq
uati
on d
5rt
,sh
own
in
th
e in
trod
uct
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,w
hat
nu
mber
is
use
dfo
r r?
for
d?
5,8
70,0
00,0
00,0
00;
311,1
10,0
00,0
00,0
00
•W
hat
equ
ati
on c
ould
you
use
to
fin
d t
he
tim
e it
tak
es l
igh
t to
rea
ch E
art
hfr
om t
he
fart
hes
t st
ar
in t
he
Big
Dip
per
?
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70,0
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00,0
00t
5821,8
00,0
00,0
00,0
00
Read
ing
th
e L
ess
on
Co
mp
lete
th
e s
en
ten
ce a
fter e
ach
eq
ua
tio
n t
o t
ell
ho
w y
ou
wo
uld
so
lve t
he
eq
ua
tio
n.
1.
516
each
sid
e by
.
2.
5x
5125
each
sid
e by
,or
mu
ltip
ly e
ach
sid
e by
.
3.
28k
596
Div
ide
each
sid
e by
,or
mu
ltip
ly e
ach
sid
e by
.
4.
Exp
lain
how
rew
riti
ng 4
x5
2as
x5
hel
ps
you
sol
ve
the
equ
ati
on.
It m
akes i
t easie
r fo
r yo
u t
o s
ee w
hat
nu
mb
er
yo
u n
eed
to
mu
ltip
ly b
y o
neach
sid
e.
Help
ing
Yo
u R
em
em
ber
5.
On
e w
ay t
o re
mem
ber
som
eth
ing i
s to
exp
lain
it
to s
omeo
ne
else
.W
rite
how
you
wou
ld
exp
lain
to
a c
lass
mate
how
to
solv
e th
e eq
uati
on
x5
12.
Sam
ple
an
sw
er:
Mu
ltip
ly e
ach
sid
e o
f th
e e
qu
ati
on
by t
he r
ecip
rocal
of
so
yo
u c
an
iso
late
xo
n t
he l
eft
sid
e.
2 } 3
2 } 3
17
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13
}3
1 } 8
1 } 3
2}1 8}
28
}1 5}5
Div
ide
7M
ult
iply
x } 7
©G
lencoe/M
cG
raw
-Hill
154
Gle
ncoe A
lgebra
1
Dis
secti
on
Pu
zzle
s:
Make t
he S
qu
are
In a
dis
sect
ion
pu
zzle
,you
are
to
cut
ap
art
on
e fi
gu
re u
sin
g o
nly
stra
igh
t cu
ts a
nd
th
en r
earr
an
ge
the
pie
ces
to m
ak
e a n
ew f
igu
re.
Usu
all
y t
he
pu
zzle
-sol
ver
mu
st f
igu
re o
ut
wh
ere
to m
ak
e th
e giv
enn
um
ber
of
cuts
.H
owev
er,fo
r th
ese
pu
zzle
s,th
e cu
t li
nes
are
sh
own
.Y
ou m
ust
dis
cover
how
to
rearr
an
ge
the
pie
ces.
Cu
t a
pa
rt
ea
ch
fig
ure.T
hen
rea
rra
ng
e t
he p
ieces
to f
orm
a s
qu
are.
1.
2. 3.
4.
Hin
t:C
ut
one
of t
he
tria
ngle
s in
to t
wo
pie
ces
to m
ak
e th
is s
qu
are
.
AA
AA
A
2x
2x
2x
x
A
A
A
A
AA
AA
B
A
A
A
A
B
2x
2x
x
x
A
C D
A
C
B
B
D
AB
B
B
B
A
B
B
B
B
En
rich
men
t
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-3
3-3
Answers (Lesson 3-3)
© Glencoe/McGraw-Hill A11 Glencoe Algebra 1
An
swers
Stu
dy G
uid
e a
nd I
nte
rven
tion
So
lvin
g M
ult
i-S
tep
Eq
uati
on
s
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-4
3-4
©G
lencoe/M
cG
raw
-Hill
155
Gle
ncoe A
lgebra
1
Lesson 3-4
Wo
rk B
ack
ward
Wo
rk
ing
ba
ck
wa
rd
is o
ne
of m
an
y p
roble
m-s
olvin
g s
trate
gie
s th
at
you
can
use
to
solv
e p
roble
ms.
To
wor
k b
ack
ward
,st
art
wit
h t
he
resu
lt g
iven
at
the
end
of
ap
roble
m a
nd
un
do
each
ste
p t
o arr
ive
at
the
beg
inn
ing n
um
ber
.
A n
um
ber i
s d
ivid
ed
by
2,
an
d t
hen
8 i
s su
btr
acte
d f
ro
mth
e q
uo
tien
t.T
he r
esu
lt i
s 16.W
ha
tis
th
e n
um
ber?
Sol
ve
the
pro
ble
m b
y w
ork
ing b
ack
ward
.
Th
e fi
nal
nu
mber
is
16.U
nd
osu
btr
act
ing 8
by a
dd
ing 8
to
get
24.T
ou
nd
o d
ivid
ing 2
4 b
y 2
,m
ult
iply
24 b
y 2
to g
et 4
8.
Th
e or
igin
al
nu
mber
is
48.
A b
acte
ria
cu
ltu
re d
ou
ble
sea
ch
ha
lf h
ou
r.A
fter 3
ho
urs,
there a
re
6400 b
acte
ria
.H
ow
ma
ny
ba
cte
ria
were
there t
o b
eg
in w
ith
?
Sol
ve
the
pro
ble
m b
y w
ork
ing b
ack
ward
.
Th
e bact
eria
have
gro
wn
for
3 h
ours
.S
ince
th
ere
are
2 o
ne-
half
hou
r p
erio
ds
in o
ne
hou
r,in
3 h
ours
ther
e are
6 o
ne-
half
hou
r p
erio
ds.
Sin
ce t
he
bact
eria
cu
ltu
re h
as
gro
wn
for
6 t
ime
per
iod
s,it
has
dou
ble
d 6
tim
es.U
nd
o th
e d
oubli
ng b
yh
alv
ing t
he
nu
mber
of
bact
eria
6 t
imes
.
6,4
00 3
33
33
35
6,4
00 3
5100
Th
ere
wer
e 100 b
act
eria
to
beg
in w
ith
.
1} 6
4
1 } 2
1 } 2
1 } 2
1 } 2
1 } 2
1 } 2
Example
1Example
1Example
2Example
2
Exercises
Exercises
So
lve e
ach
pro
ble
m b
y w
ork
ing
ba
ck
wa
rd
.
1.
A n
um
ber
is
div
ided
by 3
,an
d t
hen
4 i
s ad
ded
to
the
qu
otie
nt.
Th
e re
sult
is
8.F
ind
th
en
um
ber
.12
2.
A n
um
ber
is
mu
ltip
lied
by 5
,an
d t
hen
3 i
s su
btr
act
ed f
rom
th
e p
rod
uct
.T
he
resu
lt i
s 12.
Fin
d t
he
nu
mber
.3
3.
Eig
ht
is s
ubtr
act
ed f
rom
a n
um
ber
,an
d t
hen
th
e d
iffe
ren
ce i
s m
ult
ipli
ed b
y 2
.T
he
resu
ltis
24.F
ind
th
e n
um
ber
.20
4.
Th
ree
tim
es a
nu
mber
plu
s 3 i
s 24.F
ind
th
e n
um
ber
.7
5.C
AR
RE
NTA
LA
ngel
a r
ente
d a
car
for
$29.9
9 a
day p
lus
a o
ne-
tim
e in
sura
nce
cos
t of
$5.0
0.H
er b
ill
was
$124.9
6.F
or h
ow m
an
y d
ays
did
sh
e re
nt
the
car?
4 d
ays
6.M
ON
EY
Mik
e w
ith
dre
w a
n a
mou
nt
of m
oney
fro
m h
is b
an
k a
ccou
nt.
He
spen
t on
efo
urt
h f
or g
aso
lin
e an
d h
ad
$90 l
eft.
How
mu
ch m
oney
did
he
wit
hd
raw
?$120
7.T
ELE
VIS
ION
SIn
1999,68%
of
hou
seh
old
s w
ith
TV
’s s
ubsc
ribed
to
cable
TV
.If
8,0
00 m
ore
subsc
riber
s are
ad
ded
to
the
nu
mber
of
hou
seh
old
s w
ith
cable
,th
e to
tal
nu
mber
of
hou
seh
old
s w
ith
cable
TV
wou
ld b
e 67,6
00,0
00.H
ow m
an
y h
ouse
hol
ds
wer
e th
ere
wit
hT
V i
n 1
999?
Sourc
e:
World A
lmanac99,4
00,0
00 h
ou
seh
old
s
©G
lencoe/M
cG
raw
-Hill
156
Gle
ncoe A
lgebra
1
So
lve M
ult
i-Ste
p E
qu
ati
on
sT
o so
lve
equ
ati
ons
wit
h m
ore
than
on
e op
erati
on,of
ten
call
ed m
ult
i-st
ep
eq
ua
tio
ns,
un
do
oper
ati
ons
by w
ork
ing b
ack
ward
.R
ever
se t
he
usu
al
ord
er o
f op
erati
ons
as
you
wor
k.
So
lve 5
x1
3 5
23.
5x
13
523
Origin
al equation.
5x
13 2
35
23 2
3S
ubtr
act
3 f
rom
each s
ide.
5x
520
Sim
plif
y.
5D
ivid
e e
ach s
ide b
y 5
.
x5
4S
implif
y.
So
lve e
ach
eq
ua
tio
n.T
hen
ch
eck
yo
ur s
olu
tio
n.
1.
5x
12 5
27
52.
6x
19 5
27
33.
5x
116 5
51
7
4.
14n
28 5
34
35.
0.6
x2
1.5
51.8
5.5
6.
p2
4 5
10
16
7.
16 5
236
8.
8 1
513
20
9.
13 5
213
80
10.
510
27
11.
0.2
x2
8 5
22
30
12.
3.2
y2
1.8
53
1.5
13.
24 5
414.
8 5
212 1
280
15.
0 5
10
y2
40
4
Writ
e a
n e
qu
ati
on
an
d s
olv
e e
ach
pro
ble
m.
16.F
ind
th
ree
con
secu
tive
inte
ger
s w
hos
e su
m i
s 96.
n1
(n1
1)
1(n
12)
596;
31,32,33
17.F
ind
tw
o co
nse
cuti
ve
odd
in
teger
s w
hos
e su
m i
s 176.
n1
(n1
2)
5176;
87,89
18.
Fin
d t
hre
e co
nse
cuti
ve
inte
ger
s w
hos
e su
m i
s 2
93.
n1
(n1
1)
1(n
12)
52
93;
232,
231,
230
k} 2
43 } 7
7x
2(2
1)
}}
28
4b
18
}2
2
g} 2
5
3n
} 12
d2
12
}14
7 } 8
20
}5
5x
}5
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued)
So
lvin
g M
ult
i-S
tep
Eq
uati
on
s
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-4
3-4 Example
Example
Exercises
Exercises
Answers (Lesson 3-4)
© Glencoe/McGraw-Hill A12 Glencoe Algebra 1
Skil
ls P
racti
ce
So
lvin
g M
ult
i-S
tep
Eq
uati
on
s
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-4
3-4
©G
lencoe/M
cG
raw
-Hill
157
Gle
ncoe A
lgebra
1
Lesson 3-4
So
lve e
ach
pro
ble
m b
y w
ork
ing
ba
ck
wa
rd
.
1.
A n
um
ber
is
div
ided
by 2
,an
d t
hen
th
e qu
otie
nt
is a
dd
ed t
o 8.T
he
resu
lt i
s 33.F
ind
th
en
um
ber
.50
2.
Tw
o is
su
btr
act
ed f
rom
a n
um
ber
,an
d t
hen
th
e d
iffe
ren
ce i
s d
ivid
ed b
y 3
.T
he
resu
lt i
s30.F
ind
th
e n
um
ber
.92
3.
A n
um
ber
is
mu
ltip
lied
by 2
,an
d t
hen
th
e p
rod
uct
is
ad
ded
to
9.T
he
resu
lt i
s 49.W
hat
is t
he
nu
mber
?20
4.A
LLO
WA
NC
EA
fter
Ric
ard
o re
ceiv
ed h
is a
llow
an
ce f
or t
he
wee
k,h
e w
ent
to t
he
mall
wit
h s
ome
frie
nd
s.H
e sp
ent
half
of
his
all
owan
ce o
n a
new
pap
erback
boo
k.T
hen
he
bou
gh
t h
imse
lf a
sn
ack
for
$1.2
5.W
hen
he
arr
ived
hom
e,h
e h
ad
$5.0
0 l
eft.
How
mu
chw
as
his
all
owan
ce?
$12.5
0
So
lve e
ach
eq
ua
tio
n.T
hen
ch
eck
yo
ur s
olu
tio
n.
5.
5x
13 5
23
46.
4 5
3a
214
67.
2y
15 5
19
7
8.
6 1
5c
52
29
27
9.
8 2
5w
52
37
910.
18 2
4v
542
26
11.
28 5
22
18
12.
5 1
51
216
13.
22
4 5
13
251
14.
21
12 5
27
114
15.
22 5
955
16.
13 5
21
228
17.
q2
7 5
820
18.
g1
6 5
212
227
19.
z2
8 5
23
2
20.
m1
2 5
65
21.
53
17
22.
52
5
Writ
e a
n e
qu
ati
on
an
d s
olv
e e
ach
pro
ble
m.
23.T
wic
e a n
um
ber
plu
s fo
ur
equ
als
6.W
hat
is t
he
nu
mber
?2n
14 5
6;
1
24.S
ixte
en i
s se
ven
plu
s th
ree
tim
es a
nu
mber
.F
ind
th
e n
um
ber
.16 5
7 1
3n
;3
25.F
ind
tw
o co
nse
cuti
ve
inte
ger
s w
hos
e su
m i
s 35.
n1
(n1
1)
535;
17,18
26.F
ind
th
ree
con
secu
tive
inte
ger
s w
hos
e su
m i
s 36.
n1
(n1
1)
1(n
12)
536;
11,12,13
b1
1}
3
c2
5}
4
4 } 5
5 } 2
2 } 3
3 } 4
w } 7
a } 5
d } 6
h } 3
x } 4
n } 3
©G
lencoe/M
cG
raw
-Hill
158
Gle
ncoe A
lgebra
1
So
lve e
ach
pro
ble
m b
y w
ork
ing
ba
ck
wa
rd
.
1.
Th
ree
is a
dd
ed t
o a n
um
ber
,an
d t
hen
th
e su
m i
s m
ult
ipli
ed b
y 4
.T
he
resu
lt i
s 16.F
ind
the
nu
mber
.1
2.
A n
um
ber
is
div
ided
by 4
,an
d t
he
qu
otie
nt
is a
dd
ed t
o 3.T
he
resu
lt i
s 24.W
hat
is t
he
nu
mber
?84
3.
Tw
o is
su
btr
act
ed f
rom
a n
um
ber
,an
d t
hen
th
e d
iffe
ren
ce i
s m
ult
ipli
ed b
y 5
.T
he
resu
ltis
30.F
ind
th
e n
um
ber
.8
4.B
IRD
WA
TC
HIN
GW
hil
e M
ich
elle
sat
obse
rvin
g b
ird
s at
a b
ird
fee
der
,on
e fo
urt
h o
f th
ebir
ds
flew
aw
ay w
hen
th
ey w
ere
start
led
by a
noi
se.T
wo
bir
ds
left
th
e fe
eder
to
go
toan
oth
er s
tati
oned
a f
ew f
eet
aw
ay.
Th
ree
mor
e bir
ds
flew
in
to t
he
bra
nch
es o
f a n
earb
ytr
ee.F
our
bir
ds
rem
ain
ed a
t th
e fe
eder
.H
ow m
an
y b
ird
s w
ere
at
the
feed
er i
nit
iall
y?
12
So
lve e
ach
eq
ua
tio
n.T
hen
ch
eck
yo
ur s
olu
tio
n.
5.
212
n2
19 5
77
28
6.
17 1
3f
514
21
7.
15t
14 5
49
3
8.
16 5
22
20
9.
13 5
15
248
10.
26 5
22
12
11.
y2
52
12.
232 2
f5
217
225
13.
8 2
k5
24
32
14.
51
21
15.
52
942
16.
516
29
17.
20.5
52.5
21
18.
2.5
g1
0.4
5 5
0.9
50.2
19.
0.4
m2
0.7
50.2
22.3
Writ
e a
n e
qu
ati
on
an
d s
olv
e e
ach
pro
ble
m.
20.S
even
les
s th
an
fou
r ti
mes
a n
um
ber
equ
als
13.W
hat
is t
he
nu
mber
?4n
27 5
13;
5
21.F
ind
tw
o co
nse
cuti
ve
odd
in
teger
s w
hos
e su
m i
s 116.
n1
(n1
2)
5116;
57,59
22.F
ind
tw
o co
nse
cuti
ve
even
in
teger
s w
hos
e su
m i
s 126
.n
1(n
12)
5126;
62,64
23.F
ind
th
ree
con
secu
tive
odd
in
teger
s w
hos
e su
m i
s 11
7.
n1
(n1
2)
1(n
14)
5117;
37,39,41
24.C
OIN
CO
LLE
CT
ING
Ju
ng h
as
a t
otal
of 9
2 c
oin
s in
his
coi
n c
olle
ctio
n.T
his
is
8 m
ore
than
th
ree
tim
es t
he
nu
mber
of
qu
art
ers
in t
he
coll
ecti
on.H
ow m
an
y q
uart
ers
doe
s Ju
ng
have
in h
is c
olle
ctio
n?
28
x } 7
3k
27
}5
15 2
a}
3
r1
13
}12
3 } 8
3 } 5
7 } 8
1 } 8
1 } 2
b } 3
d} 2
4
u } 5
Pra
cti
ce (
Avera
ge)
So
lvin
g M
ult
i-S
tep
Eq
uati
on
s
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-4
3-4
Answers (Lesson 3-4)
© Glencoe/McGraw-Hill A13 Glencoe Algebra 1
An
swers
Readin
g t
o L
earn
Math
em
ati
cs
So
lvin
g M
ult
i-S
tep
Eq
uati
on
s
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-4
3-4
©G
lencoe/M
cG
raw
-Hill
159
Gle
ncoe A
lgebra
1
Lesson 3-4
Pre
-Act
ivit
yH
ow
ca
n e
qu
ati
on
s b
e u
sed
to
est
ima
te t
he a
ge o
f a
n a
nim
al?
Rea
d t
he
intr
odu
ctio
n t
o L
esso
n 3
-4 a
t th
e to
p o
f p
age
142 i
n y
our
textb
ook
.
•W
rite
th
e eq
uati
on 8
112
a5
124 i
n w
ord
s.
Eig
ht
plu
s t
welv
e t
imes a
eq
uals
on
e h
un
dre
d t
wen
ty-f
ou
r.
•H
ow m
an
y o
per
ati
ons
are
in
vol
ved
in
th
e eq
uati
on?
two
Read
ing
th
e L
ess
on
1.
Wh
at
doe
s th
e p
hra
se u
nd
o t
he
op
era
tion
sm
ean
to
you
? G
ive
an
exam
ple
.
Usin
g t
he o
pp
osit
e o
pera
tio
ns i
n t
he o
pp
osit
e o
rder
un
do
es t
he
op
era
tio
ns;
su
btr
acti
on
un
do
es a
dd
itio
n.
2.a
.If
we
un
do
oper
ati
ons
in r
ever
se o
f th
e or
der
of
oper
ati
ons,
wh
at
oper
ati
ons
do
we
do
firs
t?ad
dit
ion
or
su
btr
acti
on
b.
Wh
at
oper
ati
ons
do
we
do
last
?m
ult
iplicati
on
or
div
isio
n
3.
Su
pp
ose
you
wan
t to
sol
ve
56.
a.
Wh
at
is t
he
gro
up
ing s
ym
bol
in
th
e eq
uati
on
56?
the f
racti
on
bar
b.
Wh
at
is t
he
firs
t st
ep i
n s
olvin
g t
he
equ
ati
on?
Mu
ltip
ly e
ach
sid
e b
y 5
.
c.
Wh
at
is t
he
nex
t st
ep i
n s
olvin
g t
he
equ
ati
on?
Su
btr
act
3 f
rom
each
sid
e.
4.
Wri
te a
n e
qu
ati
on f
or t
he
pro
ble
m b
elow
.
Seven
tim
es
km
inus
five
equals
negative f
ort
y-s
even
7•
k2
55
247
Help
ing
Yo
u R
em
em
ber
5.
Exp
lain
wh
y w
ork
ing b
ack
ward
is
a u
sefu
l st
rate
gy f
or s
olvin
g e
qu
ati
ons.
Sam
ple
an
sw
er:
Yo
u c
an
un
do
th
e o
pera
tio
ns t
o g
et
back t
o t
he v
alu
e o
fth
e v
ari
ab
le t
hat
will
make t
he e
qu
ati
on
tru
e.T
hat
valu
e i
s t
he s
olu
tio
n.
x1
3}
5
x1
3}
5
©G
lencoe/M
cG
raw
-Hill
160
Gle
ncoe A
lgebra
1
Co
nsecu
tive I
nte
ger
Pro
ble
ms
Man
y t
yp
es o
f p
roble
ms
an
d p
uzz
les
invol
ve
the
idea
of
con
secu
tive
inte
ger
s.K
now
ing h
ow t
o re
pre
sen
t th
ese
inte
ger
s alg
ebra
icall
y c
an
hel
p t
o so
lve
the
pro
ble
m.
Fin
d f
ou
r c
on
secu
tiv
e o
dd
in
teg
ers
wh
ose
su
m i
s 2
80.
An
od
d i
nte
ger
can
be
wri
tten
as
2n
11,w
her
e n
is a
ny i
nte
ger
.
If 2
n +
1 i
s th
e fi
rst
odd
in
teger
,th
en a
dd
2 t
o get
th
e n
ext
larg
est
odd
inte
ger
,an
d s
o on
.
Now
wri
te a
n e
qu
ati
on t
o so
lve
this
pro
ble
m.
(2n
11)
1(2
n1
3)
1(2
n1
5)
1(2
n1
7)
52
80
Writ
e a
n e
qu
ati
on
fo
r e
ach
pro
ble
m.T
hen
so
lve.
1.
Com
ple
te t
he
solu
tion
to
the
pro
ble
m i
n t
he
exam
ple
.
223,
221,
219,
217
2.
Fin
d t
hre
e co
nse
cuti
ve
even
in
teger
s w
hos
e su
m i
s 132.
2n
1(2
n1
2)
1(2
n1
4)
5132;
n5
21;
42,44,46
3.
Fin
d t
wo
con
secu
tive
inte
ger
s w
hos
e su
m i
s 19.
n1
(n1
1)
519;
9,10
4.
Fin
d t
wo
con
secu
tive
inte
ger
s w
hos
e su
m i
s 100.
n1
(n1
1)
5100;
no
so
luti
on
5.
Th
e le
sser
of
two
con
secu
tive
even
in
teger
s is
10 m
ore
than
on
e-h
alf
th
e gre
ate
r.F
ind
th
e in
teger
s.
2n
510 1
(2n
12);
22 a
nd
24
6.
Th
e gre
ate
r of
tw
o co
nse
cuti
ve
even
in
teger
s is
6 l
ess
than
th
ree
tim
es t
he
less
er.F
ind
th
e in
teger
s.
2n
12 5
3(2
n)
26;
4,6
7.
Fin
d f
our
con
secu
tive
inte
ger
s su
ch t
hat
twic
e th
e su
m o
f th
e tw
o gre
ate
r in
teger
s ex
ceed
s th
ree
tim
es t
he
firs
t by 9
1.
2[(
n1
2)
1(n
13)]
53
n1
91;
81,82,83,84
8.
Fin
d a
set
of
fou
r co
nse
cuti
ve
pos
itiv
e in
teger
s su
ch t
hat
the
gre
ate
st i
nte
ger
in
th
e se
t is
tw
ice
the
least
in
teger
in
th
e se
t.
n1
3 5
2n
;{3
,4,5,6}
1 } 2
En
rich
men
t
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-4
3-4 Example
Example
Exercises
Exercises
Answers (Lesson 3-4)
© Glencoe/McGraw-Hill A14 Glencoe Algebra 1
Stu
dy G
uid
e a
nd I
nte
rven
tion
So
lvin
g E
qu
ati
on
s w
ith
th
e V
ari
ab
le o
n E
ach
Sid
e
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-5
3-5
©G
lencoe/M
cG
raw
-Hill
161
Gle
ncoe A
lgebra
1
Lesson 3-5
Vari
ab
les
on
Each
Sid
eT
o so
lve
an
equ
ati
on w
ith
th
e sa
me
vari
able
on
each
sid
e,fi
rst
use
th
e A
dd
itio
n o
r th
e S
ubtr
act
ion
Pro
per
ty o
f E
qu
ali
ty t
o w
rite
an
equ
ivale
nt
equ
ati
on t
hat
has
the
vari
able
on
ju
st o
ne
sid
e of
th
e eq
uati
on.T
hen
sol
ve
the
equ
ati
on.
So
lve 5
y2
8 5
3y
112.
5y
28
53y
112
5y
28 2
3y
53y
112 2
3y
2y
28
512
2y
28 1
85
12 1
8
2y
520
5
y5
10
Th
e so
luti
on i
s 10.
20
}2
2y
}2
So
lve 2
11 2
3y
58
y1
1.
211 2
3y
58y
11
211 2
3y
13y
58y
11 1
3y
211 5
11
y1
1
211 2
1 5
11
y1
1 2
1
212 5
11
y
5
21
5y
Th
e so
luti
on i
s 2
1.
1} 1
1
1} 1
1
11
y}11
212
}11
Example
1Example
1Example
2Example
2
Exercises
Exercises
So
lve e
ach
eq
ua
tio
n.T
hen
ch
eck
yo
ur s
olu
tio
n.
1.
6 2
b5
5b
130
2.
5y
22
y5
3y
12
3.
5x
12 5
2x
210
24
no
so
luti
on
24
4.
4n
28 5
3n
12
5.
1.2
x1
4.3
52.1
2x
6.
4.4
s1
6.2
58.8
s2
1.8
10
21
7.
b1
4 5
b1
88
8.
k2
5 5
k2
19.
8 2
5p
54p
21
224
81
10.4b
28 5
10 2
2b
11.
0.2
x2
8 5
22 2
x12.
3y
21.8
53y
21.8
35
all n
um
bers
13.
24 2
3x
57
x2
614.
8 1
4k
52
10 1
k15.
20 2
a
510
a2
2
26
2
16.
n1
8 5
n1
217.
y2
8 5
9 2
y18.
24r
15 5
5 2
4r
236
17
all n
um
bers
19.
24 2
3x
56
x2
620.
18 2
4k
52
10 2
4k
21.
12 1
2y
510y
212
no
so
luti
on
32 } 9
3 } 5
2 } 5
1 } 2
2 } 31 } 5
1 } 4
3 } 4
1 } 8
1 } 2
20
} 11
©G
lencoe/M
cG
raw
-Hill
162
Gle
ncoe A
lgebra
1
Gro
up
ing
Sym
bo
lsW
hen
sol
vin
g e
qu
ati
ons
that
con
tain
gro
up
ing s
ym
bol
s,fi
rst
use
the
Dis
trib
uti
ve
Pro
per
ty t
o el
imin
ate
gro
up
ing s
ym
bol
s.T
hen
sol
ve.
So
lve 4
(2a
21)
52
10(a
25).
4(2
a2
1)
52
10(a
25)
Origin
al equation
8a
24 5
210a
150
Dis
trib
utive P
ropert
y
8a
24 1
10
a
52
10a
150 1
10a
Add 1
0a
to e
ach s
ide.
18
a2
4 5
50
Sim
plif
y.
18a
24 1
4 5
50 1
4A
dd 4
to e
ach s
ide.
18a
554
Sim
plif
y.
5D
ivid
e e
ach s
ide b
y 1
8.
a5
3S
implif
y.
Th
e so
luti
on i
s 3.
So
lve e
ach
eq
ua
tio
n.T
hen
ch
eck
yo
ur s
olu
tio
n.
1.
23(x
15)
53(x
21)
2.
2(7
13t)
52
t3.
3(a
11)
25 5
3a
22
22
22
all n
um
bers
4.
75 2
9g
55(2
4 1
2g)
5.
5(f
12)
52(3
2f)
6.
4(p
13)
536
52
6
7.
18 5
3(2
c1
2)
8.
3(d
28)
53d
9.
5(p
13)
19 5
3(p
22)
16
2n
o s
olu
tio
n2
12
10.4(b
22)
52(5
2b)
11.
1.2
(x2
2)
52 2
x12.
5
32
22
13.
514.
2(4
12k)
110 5
k15.
2(w
21)
14 5
4(w
11)
24
26
21
16.6(n
21)
52(2
n1
4)
17.
2[2
13(y
21)]
522
18.
24(r
12)
54(2
24r)
74
1
19.
23(x
28)
524
20.
4(4
24k
) 5
210 2
16k
21.
6(2
22y)
55(2
y2
2)
0n
o s
olu
tio
n1
1 } 3
2a
15
}3
a2
8}
12
2y
}8
3 1
y}
4
4 } 7
54
} 18
18a
}18Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued)
So
lvin
g E
qu
ati
on
s w
ith
th
e V
ari
ab
le o
n E
ach
Sid
e
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-5
3-5 Example
Example
Exercises
Exercises
Answers (Lesson 3-5)
© Glencoe/McGraw-Hill A15 Glencoe Algebra 1
An
swers
Skil
ls P
racti
ce
So
lvin
g E
qu
ati
on
s w
ith
th
e V
ari
ab
le o
n E
ach
Sid
e
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-5
3-5
©G
lencoe/M
cG
raw
-Hill
163
Gle
ncoe A
lgebra
1
Lesson 3-5
Ju
stif
y e
ach
ste
p.
1.
4k
23 5
2k
15
4k
23 2
2k
52k
15 2
2k
a.
Su
btr
act
2k
fro
m e
ach
sid
e.
2k
23 5
5b
.S
imp
lify
.
2k
23 1
3 5
5 1
3c.
Ad
d 3
to
each
sid
e.
2k
58
d.
Sim
plify
.
5e.
Div
ide e
ach
sid
e b
y 2
.
k5
4f.
Sim
plify
.
2.
2(8
u1
2)
53(2
u2
7)
16u
14 5
6u
221
a.
Dis
trib
uti
ve P
rop
ert
y
16u
14 2
6u
56u
221 2
6u
b.
Su
btr
act
6u
fro
m e
ach
sid
e.
10u
14 5
221
c.
Sim
plify
.
10u
14 2
4 5
221 2
4d
.S
ub
tract
4 f
rom
each
sid
e.
10
u5
225
e.
Sim
plify
.
5f.
Div
ide e
ach
sid
e b
y 1
0.
u5
22.5
g.
Sim
plify
.
So
lve e
ach
eq
ua
tio
n.T
hen
ch
eck
yo
ur s
olu
tio
n.
3.
2m
112 5
3m
231
43
4.
2h
28 5
h1
17
25
5.
7a
23 5
3 2
2a
6.
4n
212 5
12 2
4n
3
7.
4x
29 5
7x
112
27
8.
26y
23 5
3 2
6y
no
so
luti
on
9.
5 1
3r
55r
219
12
10.
29 1
8k
57 1
4k
4
11.8q
112 5
4(3
12q)
all n
um
bers
12.
3(5
j1
2)
52(3
j2
6)
22
13.6(2
3v
11)
55(2
2v
22)
214.
27(2
b2
4)
55(2
2b
16)
20.5
or
2
15.3(8
23t)
55(2
1t)
116.
2(3
u1
7)
52
4(3
22u
)13
17.8(2
f2
2)
57(3
f1
2)
26
18.
5(2
6 2
3d
) 5
3(8
17d
)2
1.5
or
21
19.6(w
21)
53(3
w1
5)
27
20.
7(2
3y
12)
58(3
y2
2)
21.
v2
6 5
6 2
v9
22.
2x
5x
12
27 } 2
7 } 8
5 } 8
1 } 2
2 } 3
2 } 3
2 } 3
1 } 21 } 2
2 } 3
225
}10
10u
}10
8 } 2
2k
}2
©G
lencoe/M
cG
raw
-Hill
164
Gle
ncoe A
lgebra
1
So
lve e
ach
eq
ua
tio
n.T
hen
ch
eck
yo
ur s
olu
tio
n.
1.
5x
23 5
13 2
3x
22.
24c
211 5
4c
121
24
3.
1 2
s5
6 2
6s
14.
14 1
5n
52
4n
117
5.
k2
3 5
2 2
k4
6.
(6 2
z) 5
z2
7.
3(2
2 2
3x)
52
9x
24
no
so
luti
on
8.
4(4
2w
) 5
3(2
w1
2)
1
9.
9(4
b2
1)
52(9
b1
3)
10.
3(6
15y)
52(2
5 1
4y)
24
11.
25x
210 5
2 2
(x1
4)
22
12.
6 1
2(3
j2
2)
54(1
1j)
1
13.
t2
t5
3 1
tn
o s
olu
tio
n14.
1.4
f1
1.1
58.3
2f
3
15.
x2
5x
16
16.
2 2
z5
z1
92
8
17.
(3g
22)
518.
(c1
1)
5(3
c2
5)
7
19.
(5 2
2h
) 5
120.
(2m
216)
5(2
m1
4)
27 a
ll n
um
bers
21.3(d
28)
25 5
9(d
12)
11
28
22.
2(a
28)
17 5
5(a
12)
23a
219
23.T
wo
thir
ds
of a
nu
mber
red
uce
d b
y 1
1 i
s eq
ual
to 4
mor
e th
an
th
e n
um
ber
.F
ind
th
en
um
ber
.2
45
24.F
ive
tim
es t
he
sum
of
a n
um
ber
an
d 3
is
the
sam
e as
3 m
ult
ipli
ed b
y 1
les
s th
an
tw
ice
the
nu
mber
.W
hat
is t
he
nu
mber
?18
25.N
UM
BE
R T
HE
OR
YT
rip
lin
g t
he
gre
ate
r of
tw
o co
nse
cuti
ve
even
in
teger
s giv
es t
he
sam
ere
sult
as
subtr
act
ing 1
0 f
rom
th
e le
sser
even
in
teger
.W
hat
are
th
e in
teger
s?2
8,
26
26.G
EO
ME
TR
YT
he
form
ula
for
th
e p
erim
eter
of
a r
ecta
ngle
is
P5
2,
12w
,w
her
e ,
isth
e le
ngth
an
d w
is t
he
wid
th.A
rec
tan
gle
has
a p
erim
eter
of
24 i
nch
es.F
ind
its
dim
ensi
ons
if i
ts l
ength
is
3 i
nch
es g
reate
r th
an
its
wid
th.
4.5
in
.b
y 7
.5 i
n.
1 } 3
1 } 91 } 4
h } 2
1 } 4
1 } 6
1 } 33 } 4
g } 6
1 } 2
1 } 8
3 } 4
5 } 6
1 } 2
1 } 6
2 } 3
3 } 2
5 } 2
5 } 6
1 } 2
3 } 4
1 } 2
1 } 3
Pra
cti
ce (
Avera
ge)
So
lvin
g E
qu
ati
on
s w
ith
th
e V
ari
ab
le o
n E
ach
Sid
e
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-5
3-5
Answers (Lesson 3-5)
© Glencoe/McGraw-Hill A16 Glencoe Algebra 1
Readin
g t
o L
earn
Math
em
ati
cs
So
lvin
g E
qu
ati
on
s w
ith
th
e V
ari
ab
le o
n E
ach
Sid
e
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-5
3-5
©G
lencoe/M
cG
raw
-Hill
165
Gle
ncoe A
lgebra
1
Lesson 3-5
Pre
-Act
ivit
yH
ow
ca
n a
n e
qu
ati
on
be u
sed
to
dete
rm
ine w
hen
tw
o p
op
ula
tio
ns
are e
qu
al?
Read
th
e i
ntr
od
uct
ion
to L
ess
on
3-5
at
the t
op
of
page 1
49 i
n y
ou
r te
xtb
ook
.
In t
he e
qu
ati
on
12 1
7.6
x5
6 1
8x,w
hat
do 7
.6x
an
d 8
xre
pre
sen
t?
7.6
xre
pre
sen
ts t
he i
ncre
ase (
in m
illio
ns)
in t
he n
um
ber
of
male
In
tern
et
users
,an
d 8
xre
pre
sen
ts t
he i
ncre
ase (
inm
illio
ns)
in t
he n
um
ber
of
fem
ale
In
tern
et
users
.
Read
ing
th
e L
ess
on
1.
Su
pp
ose
you
wan
t to
help
a f
rien
d s
olv
e 6
k1
7 5
3k
28.W
hat
wou
ld y
ou
ad
vis
e h
er
to
do f
irst
? W
hy?
Su
btr
act
3k
fro
m e
ach
sid
e;
aft
er
sh
e d
oes t
hat
an
d s
imp
lifi
es,all o
f th
evari
ab
les w
ill
be o
n t
he l
eft
sid
e.
2.
Wh
en
solv
ing 2
(3x
24)5
3(x
15),
wh
y i
s it
help
ful
firs
t to
use
th
e D
istr
ibu
tive P
rop
ert
y
to r
em
ove t
he g
rou
pin
g s
ym
bols
?
On
ce y
ou
have r
em
oved
th
e g
rou
pin
g s
ym
bo
ls,yo
u c
an
tell w
hat
yo
u n
eed
to a
dd
or
su
btr
act
to e
ach
sid
e t
o g
et
all o
f th
e v
ari
ab
les o
n o
ne s
ide
.
3.
On
a q
uiz
,Jaso
n s
olv
ed
th
ree e
qu
ati
on
s.H
is t
each
er
said
all
th
e w
ork
was
corr
ect
,bu
t
she a
sked
him
to w
rite
sh
ort
sen
ten
ces
to t
ell
wh
at
the s
olu
tion
s w
ere
.In
wh
at
foll
ow
s,
you
see t
he l
ast
equ
ati
on
in
his
work
for
each
equ
ati
on
.W
rite
sen
ten
ces
to d
esc
ribe t
he
solu
tion
s.
a.
x5
24
Th
e s
olu
tio
n i
s 2
4.
b.
6m
56m
All n
um
bers
are
so
luti
on
s.
c.
12 5
37
Th
ere
are
no
so
luti
on
s.
4.
In Q
uest
ion
3,on
e o
f th
e e
qu
ati
on
s Jaso
n s
olv
ed
was
an
id
en
tity
.W
hic
h e
qu
ati
on
was
it?
Exp
lain
how
you
kn
ow
.
Th
e o
ne f
or
wh
ich
th
e l
ast
ste
p w
as 6
m5
6m
;th
e e
xp
ressio
ns o
n t
he l
eft
an
d r
igh
t sid
es a
re t
he s
am
e.
Help
ing
Yo
u R
em
em
ber
5.
An
equ
ati
on
wit
h v
ari
able
s is
an
id
en
tity
wh
en
th
e e
qu
ati
on
is
alw
ays
tru
e.In
oth
er
word
s,th
e e
xp
ress
ion
s on
th
e l
eft
an
d r
igh
t si
des
alw
ays
have t
he s
am
e v
alu
e.L
ook
up
the w
ord
id
enti
tyin
th
e d
icti
on
ary
.W
rite
all
th
e d
efi
nit
ion
s th
at
are
sim
ilar
to t
he
math
em
ati
cal
defi
nit
ion
.S
ee s
tud
en
ts’w
ork
.
©G
lencoe/M
cG
raw
-Hill
166
Gle
ncoe A
lgebra
1
Iden
titi
es
An
equ
ati
on
th
at
is t
rue f
or
every
valu
e o
f th
e v
ari
able
is
call
ed
an
iden
tity
.W
hen
you
try
to s
olv
e a
n i
den
tity
,you
en
d u
p w
ith
ast
ate
men
t th
at
is a
lways
tru
e.H
ere
is
an
exam
ple
.
So
lve 8
2(5
26x)
53(1
12x).
8 2
(5 2
6x)
53(1
12x)
8 2
5 2
(26x)
53(1
12x)
8 2
5 1
6x
53 1
6x
3 1
6x
53 1
6x
Sta
te w
heth
er e
ach
eq
ua
tio
n i
s a
n i
den
tity
.If
it
is n
ot,
fin
d i
ts s
olu
tio
n.
1.
2(2
23x)
53(3
1x)
14
2.
5(m
11)
16 5
3(4
1m
) 1
(2m
21)
x5
21
iden
tity
3.
(5t
19)
2(3
t2
13)
52(1
1 1
t)4.
14 2
(6 2
3c)
54c
2c
iden
tity
no
so
luti
on
5.
3y
22(y
119)
59y
23(9
2y)
6.
3(3
h2
1)
54(h
13)
y5
21
h5
3
7.
Use
th
e t
rue e
qu
ati
on
3x
22 5
3x
22 t
o c
reate
an
id
en
tity
of
you
r ow
n.
Sam
ple
an
sw
er:
6x
24 5
2(3
x2
2)
8.
Use
th
e f
als
e e
qu
ati
on
1 5
2 t
o c
reate
an
equ
ati
on
wit
h n
o s
olu
tion
.
Sam
ple
an
sw
er:
2x
11 5
2x
12
9.
Cre
ate
an
equ
ati
on
wh
ose
solu
tion
is
x5
3.
Sam
ple
an
sw
er:
3x
12(x
11)
520
En
rich
men
t
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D__
___
3-5
3-5 Example
Example
Exercises
Exercises
Answers (Lesson 3-5)
© Glencoe/McGraw-Hill A17 Glencoe Algebra 1
An
swers
Stu
dy G
uid
e a
nd I
nte
rven
tion
Rati
os a
nd
Pro
po
rtio
ns
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-6
3-6
©G
lencoe/M
cG
raw
-Hill
167
Gle
ncoe A
lgebra
1
Lesson 3-6
Rati
os
an
d P
rop
ort
ion
sA
ra
tio
is a
com
pari
son
of
two
nu
mber
s by d
ivis
ion
.T
he
rati
o
of x
to y
can
be
exp
ress
ed a
s x
to y
,x:y
or
.R
ati
os a
re u
suall
y e
xp
ress
ed i
n s
imp
lest
for
m.
An
equ
ati
on s
tati
ng t
hat
two
rati
os a
re e
qu
al
is c
all
ed a
pro
po
rti
on
.T
o d
eter
min
e w
het
her
two
rati
os f
orm
a p
rop
orti
on,ex
pre
ss b
oth
rati
os i
n s
imp
lest
for
m o
r ch
eck
cro
ss p
rod
uct
s.
x } y
Dete
rm
ine w
heth
er t
he
ra
tio
s a
nd
fo
rm
a p
ro
po
rti
on
.
5w
hen
exp
ress
ed i
n s
imp
lest
for
m.
5w
hen
exp
ress
ed i
n s
imp
lest
for
m.
Th
e ra
tios
an
d
form
a p
rop
orti
on
bec
au
se t
hey
are
equ
al
wh
en e
xp
ress
ed i
nsi
mp
lest
for
m.
12
} 18
24
} 36
2 } 3
12
} 18
2 } 3
24
} 36
12
} 18
24
} 36
Use
cro
ss p
ro
du
cts
to
dete
rm
ine w
heth
er
an
d
form
ap
ro
po
rti
on
.
0W
rite
the p
roport
ion.
10(4
5)
018(2
5)
Cro
ss p
roducts
450 5
450
Sim
plif
y.
Th
e cr
oss
pro
du
cts
are
equ
al,
so
5.
Sin
ce t
he
rati
os a
re e
qu
al,
they
for
m a
pro
por
tion
.
25
} 45
10
} 18
25
} 45
10
} 18
25
} 45
10
} 18
Example
1Example
1Example
2Example
2
Exercises
Exercises
Use
cro
ss p
ro
du
cts
to
dete
rm
ine w
heth
er e
ach
pa
ir o
f ra
tio
s fo
rm
s a
pro
po
rti
on
.
1.
,2.
,3.
,
yes
no
no
4.
,5.
,6.
,
no
no
yes
7.
,8.
,9.
,
yes
yes
yes
10.2
:3,20
:30
11.
5 t
o 9,25 t
o 45
12.
,
yes
yes
yes
13.5
:5,30
:20
14.
18 t
o 24,50 t
o 75
15.
100
:75,44
:33
no
no
yes
16.
,17.
,18.
,
yes
yes
yes
0.4
5}0.9
0.1
} 0.2
6 } 8
1.5
}2
1} 2
0
0.0
5}
1
9 } 8
72
} 64
20
} 30
14
} 21
9} 1
2
15
} 20
5} 1
00
0.1
}2
12
} 27
4 } 9
3} 1
6
12
} 32
15
} 20
25
} 36
25
} 49
10
} 20
10
} 15
5 } 8
16
} 32
1 } 2
©G
lencoe/M
cG
raw
-Hill
168
Gle
ncoe A
lgebra
1
So
lve P
rop
ort
ion
sIf
a p
rop
orti
on i
nvol
ves
a v
ari
able
,you
can
use
cro
ss p
rod
uct
s to
sol
ve
the
pro
por
tion
.In
th
e p
rop
orti
on
5,x
an
d 1
3 a
re c
all
ed e
xtr
em
es
an
d 5
an
d 1
0 a
re
call
ed m
ea
ns.
In a
pro
por
tion
,th
e pro
du
ct o
f th
e ex
trem
es i
s eq
ual
to t
he
pro
du
ct o
f th
e m
ean
s.
Mean
s-E
xtr
em
es P
rop
ert
y o
f P
rop
ort
ion
sF
or
any n
um
bers
a,
b,
c,
and d
, if
5,
then a
d5
bc.
So
lve
5.
5O
rigin
al pro
port
ion
13(x
) 5
5(1
0)
Cro
ss p
roducts
13
x5
50
Sim
plif
y.
5D
ivid
e e
ach s
ide b
y 1
3.
x5
3S
implif
y.
Th
e so
luti
on i
s 3
.
So
lve e
ach
pro
po
rti
on
.
1.
52
12
2.
53.
510
4.
52
5.
512
6.
51
7.
526
8.
59.
515
10.
514
11.
5n
o s
olu
tio
n12.
52
2
13.
568
14.
5n
o s
olu
tio
n15.
56
Use
a p
ro
po
rti
on
to
so
lve e
ach
pro
ble
m.
16.M
OD
ELS
To
mak
e a m
odel
of
the
Gu
ad
elou
pe
Riv
er b
ed,H
erm
ie u
sed
1 i
nch
of
clay f
or5 m
iles
of
the
river
’s a
ctu
al
len
gth
.H
is m
odel
riv
er w
as
50 i
nch
es l
ong.H
ow l
ong i
s th
eG
uad
elou
pe
Riv
er?
250 m
i
17.E
DU
CA
TIO
NJos
h f
inis
hed
24 m
ath
pro
ble
ms
in o
ne
hou
r.A
t th
at
rate
,h
ow m
an
yh
ours
wil
l it
tak
e h
im t
o co
mp
lete
72 p
roble
ms?
3 h
12
}9
2 1
w}
6
24
}k
12
}k
15
}3
a2
8}
12
2y
}8
3 1
y}
4
12
}x
1.5
}x
4} 1
2
4} b
22
p} 2
4
5 } 81 } 2
18
}3
3 } d
18
} 54
9} y
11
3} 6
3
x} 2
1
8 } x
4 } 6
3 } 4
x1
1}
4
0.5
}x
0.1
}2
3 } 55 } 3
1 } t
2 } 8
23
}x
11
} 13
11
} 13
50
} 13
13x
}13
10
} 13
x } 5
10
} 13
x } 5
c } da } b
10
} 13
x } 5
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued)
Rati
os a
nd
Pro
po
rtio
ns
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-6
3-6 Example
Example
Exercises
Exercises
Answers (Lesson 3-6)
© Glencoe/McGraw-Hill A18 Glencoe Algebra 1
Skil
ls P
racti
ce
Rati
os a
nd
Pro
po
rtio
ns
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-6
3-6
©G
lencoe/M
cG
raw
-Hill
169
Gle
ncoe A
lgebra
1
Lesson 3-6
Use
cro
ss p
ro
du
cts
to
dete
rm
ine w
heth
er e
ach
pa
ir o
f ra
tio
s fo
rm
s a
pro
po
rti
on
.W
rit
e y
es
or n
o.
1.
,yes
2.
,n
o
3.
,yes
4.
,yes
5.
,n
o6.
,yes
7.
,yes
8.
,n
o
So
lve e
ach
pro
po
rti
on
.If
necess
ary,
ro
un
d t
o t
he n
ea
rest
hu
nd
red
th.
9.
57
10.
515
11.
56
12.
518
13.
510
14.
53
15.
521
16.
518
17.
58
18.
563
19.
542
20.
544
21.
513
22.
548
23.
516
24.
560
25.B
OA
TIN
GH
ue’
s boa
t u
sed
5 g
all
ons
of g
aso
lin
e in
4 h
ours
.A
t th
is r
ate
,h
ow m
an
ygall
ons
of g
aso
lin
e w
ill
the
boa
t u
se i
n 1
0 h
ours
?12.5
gal
11
} 30
22
}x
s} 8
4
4} 2
1
20
}g
5} 1
2
27
} 39
9 } c
n} 6
0
11
} 15
30
} m
10
} 14
1 } 9
7 } b
6 } f
42
} 56
y} 6
9
6} 2
3
36
}s
12
}7
35
} 21
5 } e
3 } 5
6 } z
1 } 6
3 } a
15
} 10
9 } g
3 } 9
5 } b
2} 1
4
1 } a
50
} 85
12
} 17
21
} 98
3} 1
4
26
} 38
13
} 19
42
} 90
7} 1
6
72
} 81
8 } 9
24
} 28
6 } 7
7} 1
1
5 } 9
20
} 25
4 } 5
©G
lencoe/M
cG
raw
-Hill
170
Gle
ncoe A
lgebra
1
Use
cro
ss p
ro
du
cts
to
dete
rm
ine w
heth
er e
ach
pa
ir o
f ra
tio
s fo
rm
s a
pro
po
rti
on
.W
rit
e y
es
or n
o.
1.
,n
o2.
,n
o3.
,yes
4.
,yes
5.
,yes
6.
,yes
7.
,yes
8.
,n
o9.
,n
o
So
lve e
ach
pro
po
rti
on
.If
necess
ary,
ro
un
d t
o t
he n
ea
rest
hu
nd
red
th.
10.
59
11.
568
12.
55
13.
57
14.
518
15.
516
16.
512
17.
577
18.
51
19.
5122
20.
524
21.
57
22.
510
23.
53
24.
53
25.
51
26.
52.8
827.
51.0
2
28.
57
29.
52
30.
55
31.
532.
53
33.
54
34.PA
INT
ING
Ysi
dra
pain
ts a
roo
m t
hat
has
400 s
qu
are
fee
t of
wall
sp
ace
in
2h
ours
.A
t
this
rate
,h
ow l
ong w
ill
it t
ak
e h
er t
o p
ain
t a r
oom
th
at
has
720 s
qu
are
fee
t of
wall
space
?4
h
35.V
AC
AT
ION
PLA
NS
Walk
er i
s p
lan
nin
g a
su
mm
er v
aca
tion
.H
e w
an
ts t
o vis
it P
etri
fied
Nati
onal
For
est
an
d M
eteo
r C
rate
r,A
rizo
na,th
e 50,0
00-y
ear-
old
im
pact
sit
e of
a l
arg
em
eteo
r.O
n a
map
wit
h a
sca
le w
her
e 2 i
nch
es e
qu
als
75 m
iles
,th
e tw
o are
as
are
abou
t
1in
ches
ap
art
.W
hat
is t
he
dis
tan
ce b
etw
een
Pet
rifi
ed N
ati
onal
For
est
an
d M
eteo
r
Cra
ter?
ab
ou
t 56.2
5 m
i
1 } 2
1 } 2
1 } 24 } 7x
22
}6
3 } 7
5 } 7
r1
2}
72 } 3
x1
1}
4
5} 1
2
2 } 4
m2
1}
8
2} y
16
3} 1
2
14
}6
7} a
24
3} 0
.51
6 } n
12
}b
3} 0
.72
7} 1
.61
v} 0
.23
3 } 45 } 8
m } 63 } 5
5 } 6
3 } q
2 } 78 } c
7 } 9
2 } a
14
} 49
6 } 4
g} 1
6
12
}h
6} 6
1
z} 1
7
3} 5
1
35
}x
5} 1
1
10
} 60
2 } y
48
}9
y } 3
27
} 162
3 } u
4 } w
28
} 49
k } 7
40
} 56
34
} 23
v} 4
6
30
} 54
5 } a
3.9
} 0.9
7.6
} 1.8
2.9
} 2.4
1.7
} 1.2
7.1
4} 1
0.9
2
3.4
} 5.2
1 } 6
1.5
}9
72
} 81
8 } 9
108
}99
12
} 11
36
} 48
18
} 24
15
} 66
3} 1
1
52
} 48
7 } 6
Pra
cti
ce (
Avera
ge)
Rati
os a
nd
Pro
po
rtio
ns
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-6
3-6
Answers (Lesson 3-6)
© Glencoe/McGraw-Hill A19 Glencoe Algebra 1
An
swers
Readin
g t
o L
earn
Math
em
ati
cs
Rati
os a
nd
Pro
po
rtio
ns
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-6
3-6
©G
lencoe/M
cG
raw
-Hill
171
Gle
ncoe A
lgebra
1
Lesson 3-6
Pre
-Act
ivit
yH
ow
are r
ati
os
use
d i
n r
ecip
es?
Rea
d t
he
intr
odu
ctio
n t
o L
esso
n 3
-6 a
t th
e to
p o
f p
age
155 i
n y
our
textb
ook
.
•H
ow m
an
y s
ervin
gs
of h
oney
fro
zen
yog
urt
are
mad
e by t
his
rec
ipe?
4 s
erv
ing
s
•H
ow m
an
y r
ecip
es w
ould
be
nee
ded
to
mak
e en
ough
hon
ey f
roze
n y
ogu
rtfo
r all
th
e st
ud
ents
in
you
r cl
ass
?S
ee s
tud
en
ts’w
ork
.
Read
ing
th
e L
ess
on
1.
Com
ple
te t
he
foll
owin
g s
ente
nce
.
A r
ati
o is
a c
omp
ari
son
of
two
nu
mber
s by
.
2.
Des
crib
e tw
o w
ays
to d
ecid
e w
het
her
th
e se
nte
nce
5
is a
pro
por
tion
.
Exp
ress t
he r
ati
os i
n s
imp
lest
form
to
see i
f th
ey a
re e
qu
al.
Ch
eck t
o s
ee
wh
eth
er
the c
ross p
rod
ucts
are
eq
ual.
3.
For
each
pro
por
tion
,te
ll w
hat
the
extr
emes
are
an
d w
hat
the
mea
ns
are
.
a.
5E
xtr
emes
:M
ean
s:
b.
5E
xtr
emes
:M
ean
s:
4.
A j
et f
lyin
g a
t a s
tead
y s
pee
d t
ravel
ed 8
25 m
iles
in
2 h
ours
.If
you
sol
ved
th
e p
rop
orti
on
5,w
hat
wou
ld t
he
an
swer
tel
l you
abou
t th
e je
t?
ho
w f
ar
the j
et
travele
d i
n 1
.5 h
Help
ing
Yo
u R
em
em
ber
5.
Wri
te h
ow y
ou w
ould
exp
lain
sol
vin
g a
pro
por
tion
to
a f
rien
d w
ho
mis
sed
Les
son
3-6
.
Use c
ross p
rod
ucts
.Wri
te a
n e
qu
ati
on
wit
h t
he p
rod
uct
of
the e
xtr
em
es
on
th
e l
eft
sid
e a
nd
th
e p
rod
uct
of
the m
ean
s o
n t
he r
igh
t sid
e.T
hen
so
lve t
his
seco
nd
eq
uati
on
.
x} 1
.5
825
}2
8 a
nd
12
6 a
nd
16
12
} 16
6 } 8
35 a
nd
614 a
nd
15
6} 1
5
14
} 35
8} 2
0
2 } 5
div
isio
n
©G
lencoe/M
cG
raw
-Hill
172
Gle
ncoe A
lgebra
1
An
gle
s o
f a T
rian
gle
In g
eom
etry
,m
an
y s
tate
men
ts a
bou
t p
hysi
cal
space
are
pro
ven
to
be
tru
e.S
uch
sta
tem
ents
are
call
ed t
heo
rem
s.H
ere
are
tw
o ex
am
ple
s of
geo
met
ric
theo
rem
s.
a.
Th
e su
m o
f th
e m
easu
res
of t
he
an
gle
s of
a t
rian
gle
is
180°.
b.
If t
wo
sid
es o
f a t
rian
gle
have
equ
al
mea
sure
,th
en t
he
two
an
gle
sop
pos
ite
thos
e si
des
als
o h
ave
equ
al
mea
sure
.
Fo
r e
ach
of
the t
ria
ng
les,
writ
e a
n e
qu
ati
on
an
d t
hen
so
lve f
or x
.(A
tic
k m
ark
on
two
or m
ore s
ides
of
a t
ria
ng
le i
nd
ica
tes
tha
t th
e s
ides
ha
ve e
qu
al
mea
sure.)
1.
x5
60
82.
x5
45
8
3.
x5
45
84.
x5
20
8
5.
x5
22.5
86.
x5
10
8
7.
x5
33
88.
x5
100
8
9.
x5
60
810.
x5
50
8
11.T
wo
an
gle
s of
a t
rian
gle
have
the
sam
e12.
Th
e m
easu
re o
f on
e an
gle
of
a t
rian
gle
is
m
easu
re.T
he
sum
of
the
mea
sure
s of
tw
ice
the
mea
sure
of
a s
econ
d a
ngle
.T
he
thes
e an
gle
s is
on
e-h
alf
th
e m
easu
re o
f m
easu
re o
f th
e th
ird
an
gle
is
12 l
ess
than
th
e th
ird
an
gle
.F
ind
th
e m
easu
res
of
the
sum
of
the
oth
er t
wo.
Fin
d t
he
the
an
gle
s of
th
e tr
ian
gle
.m
easu
res
of t
he
an
gle
s of
th
e tr
ian
gle
.30
8,30
8,120
864
8,32
8,84
8
x2
x
30
°
x
40
°
x
x 2
15
°
3x
x 1
30
°
90°
4x
5x
5x
2x
x
x 1
30
°
x5
x 1
10
°
90°
x
90
°45°
x7
0°
50
°x
En
rich
men
t
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-6
3-6
Answers (Lesson 3-6)
© Glencoe/McGraw-Hill A20 Glencoe Algebra 1
Stu
dy G
uid
e a
nd I
nte
rven
tion
Perc
en
t o
f C
han
ge
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-7
3-7
©G
lencoe/M
cG
raw
-Hill
173
Gle
ncoe A
lgebra
1
Lesson 3-7
Perc
en
t o
f C
han
ge
Wh
en a
n i
ncr
ease
or
dec
rease
in
an
am
oun
t is
exp
ress
ed a
s a
per
cen
t,th
e p
erce
nt
is c
all
ed t
he
percen
t o
f ch
an
ge
.If
th
e n
ew n
um
ber
is
gre
ate
r th
an
th
eor
igin
al
nu
mber
,th
e p
erce
nt
of c
han
ge
is a
percen
t o
f in
crea
se.If
th
e n
ew n
um
ber
is
less
than
th
e or
igin
al
nu
mber
,th
e p
erce
nt
of c
han
ge
is t
he
percen
t o
f d
ecrea
se.
Fin
d t
he p
ercen
t o
f in
crea
se.
orig
ina
l:48
new
:60
Fir
st,su
btr
act
to
fin
d t
he
am
oun
t of
incr
ease
.T
he
am
oun
t of
in
crea
se i
s 60 2
48 5
12.
Th
en f
ind
th
e p
erce
nt
of i
ncr
ease
by u
sin
gth
e or
igin
al
nu
mber
,48,as
the
base
.
5P
erc
ent
pro
port
ion
12(1
00)
548(r
)C
ross p
roducts
1200 5
48r
Sim
plif
y.
5D
ivid
e e
ach s
ide b
y 4
8.
25 5
rS
implif
y.
Th
e p
erce
nt
of i
ncr
ease
is
25%
.
48r
}48
1200
}48
r} 1
00
12
} 48
Fin
d t
he p
ercen
t o
f d
ecrea
se.
orig
ina
l:30
new
:22
Fir
st,su
btr
act
to
fin
d t
he
am
oun
t of
dec
rease
.T
he
am
oun
t of
dec
rease
is
30 2
22 5
8.
Th
en f
ind
th
e p
erce
nt
of d
ecre
ase
by u
sin
gth
e or
igin
al
nu
mber
,30,as
the
base
.
5P
erc
ent
pro
port
ion
8(1
00)
530(r
)C
ross p
roducts
800 5
30r
Sim
plif
y.
5D
ivid
e e
ach s
ide b
y 3
0.
26
5r
Sim
plif
y.
Th
e p
erce
nt
of d
ecre
ase
is
26
%,or
abou
t27%
.
2 } 3
2 } 3
30r
}30
800
}30
r} 1
00
8} 3
0
Example
1Example
1Example
2Example
2
Exercises
Exercises
Sta
te w
heth
er e
ach
percen
t o
f ch
an
ge i
s a
percen
t o
f in
crea
se o
r a
percen
t o
fd
ecrea
se.T
hen
fin
d e
ach
percen
t o
f ch
an
ge.
Ro
un
d t
o t
he n
ea
rest
wh
ole
percen
t.
1.
orig
inal:
50
2.
orig
inal:
90
3.
orig
inal:
45
new
:80
new
:100
new
:20
incre
ase;
60%
incre
ase:
11%
decre
ase;
56%
4.
orig
inal:
77.5
5.
orig
inal:
140
6.
orig
inal:
135
new
:62
new
:150
new
:90
decre
ase;
20%
incre
ase:
7%
decre
ase;
33%
7.
orig
inal:
120
8.
orig
inal:
90
9.
orig
inal:
27.5
new
:180
new
:270
new
:25
incre
ase;
50%
incre
ase:
200%
decre
ase;
9%
10.or
igin
al:
84
11.
orig
inal:
12.5
12.
orig
inal:
250
new
:98
new
:10
new
:500
incre
ase;
17%
decre
ase:
20%
incre
ase;
100%
©G
lencoe/M
cG
raw
-Hill
174
Gle
ncoe A
lgebra
1
So
lve P
rob
lem
sD
isco
un
ted
pri
ces
an
d p
rice
s in
clu
din
g t
ax a
re a
pp
lica
tion
s of
per
cen
tof
ch
an
ge.
Dis
cou
nt
is t
he
am
oun
t by w
hic
h t
he
regu
lar
pri
ce o
f an
ite
m i
s re
du
ced
.T
hu
s,th
e d
isco
un
ted
pri
ce i
s an
exam
ple
of
per
cen
t of
dec
rease
.S
ale
s ta
x i
s am
oun
t th
at
is a
dd
edto
th
e co
st o
f an
ite
m,so
th
e p
rice
in
clu
din
g t
ax i
s an
exam
ple
of
per
cen
t of
in
crea
se.
A c
oa
t is
on
sa
le f
or 2
5%
off
th
e o
rig
ina
l p
ric
e.
If t
he o
rig
ina
l p
ric
eo
f th
e c
oa
t is
$75,
wh
at
is t
he d
isco
un
ted
pric
e?
Th
e d
isco
un
t is
25%
of
the
orig
inal
pri
ce.
25%
of
$75 5
0.2
5 3
75
25%
50.2
5
518.7
5U
se a
calc
ula
tor.
Su
btr
act
$18.7
5 f
rom
th
e or
igin
al
pri
ce.
$75 2
$18.7
5 5
$56.2
5
Th
e d
isco
un
ted
pri
ce o
f th
e co
at
is $
56.2
5.
Fin
d t
he f
ina
l p
ric
e o
f ea
ch
ite
m.W
hen
a d
isco
un
t a
nd
a s
ale
s ta
x a
re l
iste
d,
co
mp
ute
th
e d
isco
un
t p
ric
e b
efo
re c
om
pu
tin
g t
he t
ax
.
1.
Com
pact
dis
c:$16
2.
Tw
o co
nce
rt t
ick
ets:
$28
3.
Air
lin
e ti
cket
:$248.0
0D
isco
un
t:15%
Stu
den
t d
isco
un
t:28%
Su
per
air
dis
cou
nt:
33%
$13.6
0$20.1
6$166.1
6
4.
Sh
irt:
$24.0
05.
CD
pla
yer
:$142.0
06.
Cel
ebri
ty c
ale
nd
ar:
$10.9
5S
ale
s ta
x:4%
Sale
s ta
x:5.5
%S
ale
s ta
x:7.5
%
$24.9
6$149.8
1$11.7
7
7.
Cla
ss r
ing:$89.0
08.
Sof
tware
:$44.0
09.
Vid
eo r
ecor
der
:$110.9
5G
rou
p d
isco
un
t:17%
Dis
cou
nt:
21%
Dis
cou
nt:
20%
Sale
s ta
x:5%
Sale
s ta
x:6%
Sale
s ta
x:5%
$77.5
6$36.8
5$93.2
0
10.V
IDE
OS
Th
e or
igin
al
sell
ing p
rice
of
a n
ew s
por
ts v
ideo
wa
s $65.0
0.D
ue
to t
he
dem
an
dth
e p
rice
was
incr
ease
d t
o $87.7
5.W
hat
was
the
per
cen
t of
in
crea
se o
ver
th
e or
igin
al
pri
ce?
35%
11.S
CH
OO
LA
hig
h s
choo
l p
ap
er i
ncr
ease
d i
ts s
ale
s by 7
5%
wh
en i
t ra
n a
n i
ssu
e fe
atu
rin
ga c
onte
st t
o w
in a
cla
ss p
art
y.B
efor
e th
e co
nte
st i
ssu
e,10%
of
the
sch
ool’s
800 s
tud
ents
bou
gh
t th
e p
ap
er.H
ow m
an
y s
tud
ents
bou
gh
t th
e co
nte
st i
ssu
e?140 s
tud
en
ts
12.B
AS
EB
ALL
Base
ball
tic
ket
s co
st $
15 f
or g
ener
al
ad
mis
sion
or
$20 f
or b
ox s
eats
.T
he
sale
s ta
x o
n e
ach
tic
ket
is
8%
,an
d t
he
mu
nic
ipal
tax o
n e
ach
tic
ket
is
an
ad
dit
ion
al
10%
of t
he
base
pri
ce.W
hat
is t
he
fin
al
cost
of
each
typ
e of
tic
ket
?$17.7
0;
$23.6
0
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued)
Perc
en
t o
f C
han
ge
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-7
3-7 Example
Example
Exercises
Exercises
Answers (Lesson 3-7)
© Glencoe/McGraw-Hill A21 Glencoe Algebra 1
An
swers
Skil
ls P
racti
ce
Perc
en
t o
f C
han
ge
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-7
3-7
©G
lencoe/M
cG
raw
-Hill
175
Gle
ncoe A
lgebra
1
Lesson 3-7
Sta
te w
heth
er e
ach
percen
t o
f ch
an
ge i
s a
percen
t o
f in
crea
se o
r a
percen
t o
fd
ecrea
se.T
hen
fin
d e
ach
percen
t o
f ch
an
ge.
Ro
un
d t
o t
he n
ea
rest
wh
ole
percen
t.
1.
orig
inal:
25
2.
orig
inal:
50
new
:10
new
:75
decre
ase;
60%
incre
ase;
50%
3.
orig
inal:
55
4.
orig
inal:
25
new
:50
new
:28
decre
ase;
9%
incre
ase;
12%
5.
orig
inal:
50
6.
orig
inal:
90
new
:30
new
:95
decre
ase;
40%
incre
ase;
6%
7.
orig
inal:
48
8.
orig
inal:
60
new
:60
new
:45
incre
ase;
25%
decre
ase;
25%
Fin
d t
he t
ota
l p
ric
e o
f ea
ch
ite
m.
9.
dre
ss:$69.0
010.
bin
der
:$14.5
0ta
x:5%
tax:7%
$72.4
5$15.5
2
11.h
ard
cover
boo
k:$28.9
512.
gro
ceri
es:$47.5
2ta
x:6%
tax:3%
$30.6
9$48.9
5
13.fi
ller
pap
er:$6.0
014.
shoe
s:$65.0
0ta
x:6.5
%ta
x:4%
$6.3
9$67.6
0
15.bask
etball
:$17.0
016.
con
cert
tic
ket
s:$48.0
0ta
x:6%
ta
x:7.5
%
$18.0
2$51.6
0
Fin
d t
he d
isco
un
ted
pric
e o
f ea
ch
ite
m.
17.back
pack
:$56.2
518.
mon
itor
:$150.0
0d
isco
un
t:20%
dis
cou
nt:
50%
$45.0
0$75.0
0
19.C
D:$15.9
920.
shir
t:$25.5
0d
isco
un
t:20%
dis
cou
nt:
40%
$12.7
9$15.3
0
21.sl
eep
ing b
ag:$125
22.
coff
ee m
ak
er:$102.0
0d
isco
un
t:25%
dis
cou
nt:
45%
$93.7
5$56.1
0
©G
lencoe/M
cG
raw
-Hill
176
Gle
ncoe A
lgebra
1
Sta
te w
heth
er e
ach
percen
t o
f ch
an
ge i
s a
percen
t o
f in
crea
se o
r a
percen
t o
fd
ecrea
se.T
hen
fin
d e
ach
percen
t o
f ch
an
ge.
Ro
un
d t
o t
he n
ea
rest
wh
ole
percen
t.
1.
orig
inal:
18
2.
orig
inal:
140
3.
orig
inal:
200
new
:10
new
:160
new
:320
decre
ase;
44%
incre
ase;
14%
incre
ase;
60%
4.
orig
inal:
10
5.
orig
inal:
76
6.
orig
inal:
128
new
:25
new
:60
new
:120
incre
ase;
150%
decre
ase;
21%
decre
ase;
6%
7.
orig
inal:
15
8.
orig
inal:
98.6
9.
orig
inal:
58.8
new
:35.5
new
:64
new
:65.7
incre
ase;
137%
decre
ase;
35%
incre
ase;
12%
Fin
d t
he t
ota
l p
ric
e o
f ea
ch
ite
m.
10.co
ncr
ete
blo
cks:
$95.0
011.
crib
:$240.0
012.
jack
et:$125.0
0ta
x:6%
tax:6.5
%ta
x:5.5
%
$100.7
0$255.6
0$131.8
8
13.cl
ass
rin
g:$325.0
014.
bla
nk
et:$24.9
915.
kit
e:$18.9
0ta
x:6%
tax:7%
tax:5%
$344.5
0$26.7
4$19.8
5
Fin
d t
he d
isco
un
ted
pric
e o
f ea
ch
ite
m.
16.d
ry c
lean
ing:$25.0
017.
com
pu
ter
gam
e:$49.9
918.
luggage:
$185.0
0d
isco
un
t:15%
dis
cou
nt:
25%
dis
cou
nt:
30%
$21.2
5$37.4
9$129.5
0
19.st
ati
oner
y:$12.9
520.
pre
scri
pti
on g
lass
es:$149
21.
pair
of
shor
ts:$24.9
9
dis
cou
nt:
10%
dis
cou
nt:
20%
dis
cou
nt:
45%
$11.6
6$119.2
0$13.7
4
Fin
d t
he f
ina
l p
ric
e o
f ea
ch
ite
m.
22.te
levis
ion
:$375.0
023.
DV
D p
layer
:$269.0
024.
pri
nte
r:$255.0
0d
isco
un
t:25%
dis
cou
nt:
20%
dis
cou
nt:
30%
tax:6%
tax:7%
tax:5.5
%
$298.1
3$230.2
6$188.3
2
25.IN
VE
ST
ME
NT
ST
he
pri
ce p
er s
hare
of
an
in
tern
et-r
elate
d s
tock
dec
rease
d f
rom
$90 p
ersh
are
to
$36 p
er s
hare
earl
y i
n 2
001.B
y w
hat
per
cen
t d
id t
he
pri
ce o
f th
e st
ock
dec
rease
?60%
26.H
EA
TIN
G C
OS
TS
Cu
stom
ers
of a
uti
lity
com
pan
y r
ecei
ved
not
ices
in
th
eir
mon
thly
bil
lsth
at
hea
tin
g c
osts
for
th
e aver
age
cust
omer
had
in
crea
sed
125%
over
last
yea
r bec
au
seof
an
un
usu
all
y s
ever
e w
inte
r.In
Jan
uary
of
last
yea
r,th
e G
arc
ia’s
paid
$120 f
or h
eati
ng.
Wh
at
shou
ld t
hey
exp
ect
to p
ay t
his
Jan
uary
if
thei
r bil
l in
crea
sed
by 1
25%
?$270
Pra
cti
ce (
Avera
ge)
Perc
en
t o
f C
han
ge
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-7
3-7
Answers (Lesson 3-7)
© Glencoe/McGraw-Hill A22 Glencoe Algebra 1
Readin
g t
o L
earn
Math
em
ati
cs
Perc
en
t o
f C
han
ge
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-7
3-7
©G
lencoe/M
cG
raw
-Hill
177
Gle
ncoe A
lgebra
1
Lesson 3-7
Pre
-Act
ivit
yH
ow
ca
n p
ercen
ts d
escrib
e g
ro
wth
ov
er t
ime?
Rea
d t
he
intr
odu
ctio
n t
o L
esso
n 3
-7 a
t th
e to
p o
f p
age
160 i
n y
our
textb
ook
.
•H
ow m
an
y a
rea c
odes
wer
e in
use
in
1947?
84 a
rea c
od
es
•H
ow m
an
y m
ore
are
a c
odes
wer
e in
use
in
1999?
201 a
rea c
od
es
Read
ing
th
e L
ess
on
1.
If y
ou u
se (
orig
inal
am
oun
t) —
(n
ew a
mou
nt)
to
fin
d t
he
chan
ge
for
a p
erce
nt
of c
han
ge
pro
ble
m,th
en t
he
pro
ble
m i
nvol
ves
a p
erce
nt
of
(in
crea
se/d
ecre
ase
).
2.
If y
ou u
se (
new
am
oun
t) —
(or
igin
al
am
oun
t) t
o fi
nd
th
e ch
an
ge
for
a p
erce
nt
of c
han
ge
pro
ble
m,th
en t
he
pro
ble
m i
nvol
ves
a p
erce
nt
of
(in
crea
se/d
ecre
ase
).
Co
mp
lete
th
e c
ha
rt.
Ori
gin
al
New
P
erc
en
t In
cre
ase o
r
Am
ou
nt
Am
ou
nt
Perc
en
t P
rop
ort
ion
Perc
en
t D
ecre
ase?
3.
10
13
5in
cre
ase
4.
10
75
decre
ase
5.
50
42
5d
ecre
ase
6.
50
58
5in
cre
ase
7.
Wh
en y
ou f
ind
a d
isco
un
t p
rice
,d
o you
ad
d t
o or
su
btr
act
fro
m t
he
orig
inal
pri
ce?
su
btr
act
Help
ing
Yo
u R
em
em
ber
8.
If y
ou r
emem
ber
on
ly t
wo
thin
gs
abou
t th
e ra
tio
use
d f
or f
ind
ing p
erce
nt
of c
han
ge,
wh
at
shou
ld t
hey
be?
Su
btr
act
the p
rices,
then
div
ide b
y t
he o
rig
inal
nu
mb
er.
r}
8}
→ →
ch
an
ge
}
r}
8}
→ →
ch
an
ge
}
r}
3}
→ →
ch
an
ge
}
r}
3}
→ →
ch
an
ge
}
incre
ase
decre
ase
©G
lencoe/M
cG
raw
-Hill
178
Gle
ncoe A
lgebra
1
Usin
g P
erc
en
t
Use w
ha
t y
ou
ha
ve l
ea
rn
ed
ab
ou
t p
ercen
t to
so
lve e
ach
pro
ble
m.
A T
V m
ovie
had
a “
rati
ng”
of 1
5 a
nd
a 2
5 “
share
.”T
he
rati
ng i
s th
e p
erce
nta
ge
of t
he
nati
on’s
tot
al
TV
hou
seh
old
s th
at
wer
e tu
ned
in
to
this
sh
ow.T
he
share
is t
he
per
cen
tage
of h
omes
wit
h T
Vs
turn
ed o
n t
hat
wer
e tu
ned
to
the
mov
ie.
How
man
y T
V h
ouse
hol
ds
had
th
eir
TV
s tu
rned
off
at
this
tim
e?
To
fin
d o
ut,
let
T5
the
nu
mber
of
TV
hou
seh
old
san
d x
5th
e n
um
ber
of
TV
hou
seh
old
s w
ith
th
e T
V o
ff.
Th
en T
2x
5th
e n
um
ber
of
TV
hou
seh
old
s w
ith
th
e T
V o
n.
Sin
ce 0
.15T
an
d 0
.25(T
2x)
bot
h r
epre
sen
t th
e n
um
ber
of
hou
seh
old
s tu
ned
to t
he
mov
ie, 0
.15T
50.2
5(T
2x)
0.1
5T
50.2
5T
20.2
5x.
Sol
ve
for
x.
0.2
5x
50.1
0T
x5
50.4
0T
For
ty p
erce
nt
of t
he
TV
hou
seh
old
s h
ad
th
eir
TV
s of
f w
hen
th
e m
ovie
was
air
ed.
An
sw
er e
ach
qu
esti
on
.
1.
Du
rin
g t
hat
sam
e w
eek
,a s
por
ts b
road
cast
had
a r
ati
ng o
f 22.1
an
d a
43 s
hare
.S
how
th
at
the
per
cen
t of
TV
hou
seh
old
s w
ith
th
eir
TV
s of
f w
as
abou
t 48.6
%.
0.2
21T
50.4
3T
20.4
3x
x5 5
0.4
86
T
2.
Fin
d t
he
per
cen
t of
TV
hou
seh
old
s w
ith
th
eir
TV
s tu
rned
off
du
rin
g a
sh
ow
wit
h a
rati
ng o
f 18.9
an
d a
29 s
hare
.34.8
%
3.
Sh
ow t
hat
if T
is
the
nu
mber
of
TV
hou
seh
old
s,r
is t
he
rati
ng,an
d s
is
the
share
,th
en t
he
nu
mber
of
TV
hou
seh
old
s w
ith
th
e T
V o
ff i
s .
So
lve r
T5
s(T
2x
) fo
r x.
4.
If t
he
fract
ion
of
TV
hou
seh
old
s w
ith
no
TV
on
is
then
sh
ow t
hat
the
fract
ion
of
TV
hou
seh
old
s w
ith
TV
s on
is
.
5.
Fin
d t
he
per
cen
t of
TV
hou
seh
old
s w
ith
TV
s on
du
rin
g t
he
mos
t w
atc
hed
se
rial
pro
gra
m i
n h
isto
ry:th
e la
st e
pis
ode
of M
*A*S
*H,w
hic
h h
ad
a 6
0.3
ra
tin
g a
nd
a 7
7 s
hare
.5
78.3
%
6.A
loc
al
stati
on n
ow h
as
a 2
sh
are
.E
ach
sh
are
is
wor
th $
50,0
00 i
n a
dver
tisi
ng
reven
ue
per
mon
th.T
he
stati
on i
s th
ink
ing o
f goi
ng c
omm
erci
al
free
for
th
e th
ree
mon
ths
of s
um
mer
to
gain
mor
e li
sten
ers.
Wh
at
wou
ld i
ts n
ew s
hare
h
ave
to b
e fo
r th
e la
st 4
mon
ths
of t
he
yea
r to
mak
e m
ore
mon
ey f
or t
he
yea
r th
an
it
wou
ld h
ave
mad
e h
ad
it
not
gon
e co
mm
erci
al
free
?g
reate
r th
an
3.5
60.3
}
r } s
s –
r}
s
(s2
r)T
}
s
0.2
21T
20.4
3T
}}
0.1
0T
}
0.2
5
En
rich
men
t
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D__
___
3-7
3-7
1 2
5r }
s2
r}
Answers (Lesson 3-7)
© Glencoe/McGraw-Hill A23 Glencoe Algebra 1
An
swers
Stu
dy G
uid
e a
nd I
nte
rven
tion
So
lvin
g E
qu
ati
on
s a
nd
Fo
rmu
las
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-8
3-8
©G
lencoe/M
cG
raw
-Hill
179
Gle
ncoe A
lgebra
1
Lesson 3-8
So
lve f
or
Vari
ab
les
Som
etim
es y
ou m
ay w
an
t to
sol
ve
an
equ
ati
on s
uch
as
V5
,w
hfo
ron
e of
its
vari
able
s.F
or e
xam
ple
,if
you
kn
ow t
he
valu
es o
f V
,w
,an
d h
,th
en t
he
equ
ati
on
,5
is m
ore
use
ful
for
fin
din
g t
he
valu
e of
,.If
an
equ
ati
on t
hat
con
tain
s m
ore
than
on
e
vari
able
is
to b
e so
lved
for
a s
pec
ific
vari
able
,u
se t
he
pro
per
ties
of
equ
ali
ty t
o is
olate
th
esp
ecif
ied
vari
able
on
on
e si
de
of t
he
equ
ati
on.
V} w
h
So
lve 2
x2
4y
58 f
or y
.
2x
24y
58
2x
24y
22x
58 2
2x
24y
58 2
2x
5
y5
or
Th
e valu
e of
yis
.
2x
28
}4
2x
28
}4
8 2
2x
}2
4
8 2
2x
}2
4
24y
}2
4
So
lve 3
m2
n5
km
28 f
or m
.
3m
2n
5km
28
3m
2n
2km
5km
28 2
km
3m
2n
2km
52
83m
2n
2km
1n
52
8 1
n
3m
2km
52
8 1
n
m(3
2k)
52
8 1
n
5
m5
,or
Th
e valu
e of
mis
.S
ince
div
isio
n b
y 0
is
un
def
ined
,3 2
kÞ
0,or
kÞ
3.
n2
8} 3
2k
n2
8} 3
2k
28 1
n}
3 2
k
28 1
n}
3 2
k
m(3
2k)
}}
3 2
k
Example
1Example
1Example
2Example
2
Exercises
Exercises
So
lve e
ach
eq
ua
tio
n o
r f
orm
ula
fo
r t
he v
aria
ble
sp
ecif
ied
.
1.
ax
2b
5c
for
x2.
15x
11 5
yfo
r x
3.
(x1
f) 1
2 5
jfo
r x
x5
,a
Þ0
x5
x5
j2
2 2
f
4.
xy
1z
59 f
or y
5.
x(4
2k)
5p
for
k6.
7x
13y
5m
for
y
y5
,x
Þ0
k5
4 2
,x
Þ0
y5
7.
4(c
13)
5t
for
c8.
2x
1b
5c
for
x9.
x(1
1y)
5z
for
x
c5
23
x5
x5
,y
Þ2
1
10.16
z1
4x
5y
for
x11.
d5
rtfo
r r
12.
A5
for
h
x5
r5
,t
Þ0
h5
,a
Þ2
b
13.C
5(F
232)
for
F14.
P5
2,
12w
for
w15.
A5
,w
for
,
F5
C1
32
w5
,5
,w
Þ0
A } w
P2
2,
}2
9 } 5
5 } 9
2A
} a1
bd } t
y2
16
z}
4
h(a
1b)
}} 2z
} 1 1
y
c2
b}
2t } 4
m2
7x
}3
p } x
9 2
z}
x
y2
1}
15
c1
b}
a
©G
lencoe/M
cG
raw
-Hill
180
Gle
ncoe A
lgebra
1
Use
Fo
rmu
las
Man
y r
eal-
wor
ld p
roble
ms
requ
ire
the
use
of
form
ula
s.S
omet
imes
sol
vin
ga f
orm
ula
for
a s
pec
ifie
d v
ari
able
wil
l h
elp
sol
ve
the
pro
ble
m.
Th
e f
orm
ula
C5
pd
rep
rese
nts
th
e c
ircu
mfe
ren
ce o
f a
cir
cle
,o
r t
he
dis
tan
ce a
ro
un
d t
he c
ircle
,w
here d
is t
he d
iam
ete
r.If
an
air
pla
ne c
ou
ld f
ly a
ro
un
dE
arth
at
the e
qu
ato
r w
ith
ou
t st
op
pin
g,
it w
ou
ld h
av
e t
ra
vele
d a
bo
ut
24,9
00 m
iles.
Fin
d t
he d
iam
ete
r o
f E
arth
.
C5
pd
Giv
en f
orm
ula
d5
Solv
e f
or
d.
d5
Use p
53.1
4.
d<
7930
Sim
plif
y.
Th
e d
iam
eter
of
Eart
h i
s abou
t 7930 m
iles
.
1.G
EO
ME
TR
YT
he
vol
um
e of
a c
yli
nd
er V
is g
iven
by t
he
form
ula
V5
pr2
h,w
her
e r
isth
e ra
diu
s an
d h
is t
he
hei
gh
t.
a.
Sol
ve
the
form
ula
for
h.
h5
b.
Fin
d t
he
hei
gh
t of
a c
yli
nd
er w
ith
vol
um
e 2500
pfe
et a
nd
rad
ius
10 f
eet.
25 f
t
2.W
AT
ER
PR
ES
SU
RE
Th
e w
ate
r p
ress
ure
on
a s
ubm
erged
obje
ct i
s giv
en b
y P
564d
,w
her
e P
is t
he
pre
ssu
re i
n p
oun
ds
per
squ
are
foo
t,an
d d
is t
he
dep
th o
f th
e ob
ject
in
fee
t.
a.
Sol
ve
the
form
ula
for
d.
d5
b.
Fin
d t
he
dep
th o
f a s
ubm
erged
obje
ct i
f th
e p
ress
ure
is
672 p
oun
ds
per
squ
are
foo
t.10.5
ft
3.G
RA
PH
ST
he
equ
ati
on o
f a l
ine
con
tain
ing t
he
poi
nts
(a
,0)
an
d (
0,b)
is g
iven
by t
he
form
ula
1
51.
a.
Sol
ve
the
equ
ati
on f
or y
.y
5b
11 2
2b
.S
up
pos
e th
e li
ne
con
tain
s th
e p
oin
ts (
4,0),
an
d (
0,
22).
If x
53,fi
nd
y.
2
4.G
EO
ME
TR
YT
he
surf
ace
are
a o
f a r
ecta
ngu
lar
soli
d i
s giv
en b
y t
he
form
ula
S
52
,w
12
,h
12w
h,w
her
e ,
5le
ngth
,w
5w
idth
,an
d h
5h
eigh
t.
a.
Sol
ve
the
form
ula
for
h.
h5
b.
Th
e su
rface
are
a o
f a r
ecta
ngu
lar
soli
d w
ith
len
gth
6 c
enti
met
ers
an
d w
idth
3 c
enti
met
ers
is 7
2 s
qu
are
cen
tim
eter
s.F
ind
th
e h
eigh
t.2 c
m
S2
2,w
}}
2,
12w
1 } 2
x } a
y } b
x } a
P } 64V
} pr
2
24,9
00
}3.1
4
C } p
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued)
So
lvin
g E
qu
ati
on
s a
nd
Fo
rmu
las
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-8
3-8 Example
Example
Exercises
Exercises
Answers (Lesson 3-8)
© Glencoe/McGraw-Hill A24 Glencoe Algebra 1
Skil
ls P
racti
ce
So
lvin
g E
qu
ati
on
s a
nd
Fo
rmu
las
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-8
3-8
©G
lencoe/M
cG
raw
-Hill
181
Gle
ncoe A
lgebra
1
Lesson 3-8
So
lve e
ach
eq
ua
tio
n o
r f
orm
ula
fo
r t
he v
aria
ble
sp
ecif
ied
.
1.
7t
5x,fo
r t
t5
2.
e5
wp
,fo
r p
p5
3.
q2
r5
r,fo
r r
r5
4.
4m
2n
5m
,fo
r m
m5
5.
7a
2b
515
a,fo
r a
a5
26.
25c
1d
52c,
for
cc
5
7.
x2
2y
51,fo
r y
y5
8.
m 1
3n
51,fo
r n
n5
9.
7f
1g
55,fo
r f
f5
10.
ax
2c
5b,fo
r x
x5
11.rt
22n
5y,fo
r t
t5
12.
bc
13g
52k,fo
r c
c5
13.kn
14f
59v,fo
r n
n5
14.
8c
16j
55
p,fo
r c
c5
15.
5d
,fo
r x
x5
c1
2d
16.
5d
,fo
r c
c5
x2
2d
17.
5q,fo
r p
p5
5q
29
18.
5a
,fo
r b
b5
7a 1
4z
Writ
e a
n e
qu
ati
on
an
d s
olv
e f
or t
he v
aria
ble
sp
ecif
ied
.
19.F
ive
mor
e th
an
a n
um
ber
gis
six
les
s th
an
tw
ice
a n
um
ber
h.S
olve
for
g.
g 1
5 5
2h
26;
g5
2h
211
20.O
ne
fou
rth
of
a n
um
ber
qis
th
ree
mor
e th
an
th
ree
tim
es a
nu
mber
w.S
olve
for
q.
q5
3w
13;
q5
12
w1
12
21.E
igh
t le
ss t
han
a n
um
ber
sis
th
ree
mor
e th
an
fou
r ti
mes
a n
um
ber
t.S
olve
for
s.
s2
8 5
4t
13;
s5
4t
111
1 } 4
b2
4z
}7
p1
9}
5
x2
c}
2
x2
c}
2
5p
26j
}8
9v
24f
}k
2k
23
g}
b
2n
1y
}r
b1
c}
a
5 2
g}
7
1 2
m}
3x
21
}2
d } 7b } 8
n } 3
q } 2
e } wx } 7
©G
lencoe/M
cG
raw
-Hill
182
Gle
ncoe A
lgebra
1
So
lve e
ach
eq
ua
tio
n o
r f
orm
ula
fo
r t
he v
aria
ble
sp
ecif
ied
.
1.
d5
rt,fo
r r
r5
2.
6w
2y
52z,
for
ww
5
3.
mx
14
y5
3c,
for
xx
54.
9s
25g
52
4u
,fo
r s
s5
5.
ab
13c
52d
,fo
r b
b5
6.
2p
5kx
2q,fo
r x
x5
7.
m1
a5
a1
c,fo
r m
m5
c8.
h1
g5
d,fo
r h
h5
(d2
g)
9.
y1
v5
s,fo
r y
y5
(s2
v)
10.
a2
q5
k,fo
r a
a5
(k1
q)
11.
5h
,fo
r x
x5
12.
5c,
for
bb
5
13.2
w2
y5
7w
22,fo
r w
w5
14.
3,
1y
55 1
5,,fo
r ,
,5
Writ
e a
n e
qu
ati
on
an
d s
olv
e f
or t
he v
aria
ble
sp
ecif
ied
.
15.T
hre
e ti
mes
a n
um
ber
sp
lus
4 t
imes
a n
um
ber
yis
1 m
ore
than
6 t
imes
th
e n
um
ber
s.
Sol
ve
for
s.
3s
14y
56s
11;
s5
16.F
ive
tim
es a
nu
mber
km
inu
s 9 i
s tw
o th
ird
s of
a n
um
ber
j.S
olve
for
j.
5k
29 5
j;j
5(5
k2
9)
ELE
CT
RIC
ITY
Fo
r E
xercis
es
17 a
nd
18,
use
th
e f
oll
ow
ing
in
form
ati
on
.
Th
e fo
rmu
la f
or O
hm
’s L
aw
is
E5
IR,w
her
e E
rep
rese
nts
vol
tage
mea
sure
d i
n v
olts
,I
rep
rese
nts
cu
rren
t m
easu
red
in
am
per
es,an
d R
rep
rese
nts
res
ista
nce
mea
sure
d i
n o
hm
s.
17.S
olve
the
form
ula
for
R.
R5
18.S
up
pos
e a c
urr
ent
of 0
.25 a
mp
ere
flow
s th
rou
gh
a r
esis
tor
con
nec
ted
to
a 1
2-v
olt
batt
ery.
Wh
at
is t
he
resi
stan
ce i
n t
he
circ
uit
?48 o
hm
s
MO
TIO
NF
or E
xercis
es
19 a
nd
20,
use
th
e f
oll
ow
ing
in
form
ati
on
.
In u
nif
orm
cir
cula
r m
oti
on
,th
e sp
eed
vof
a p
oin
t on
th
e ed
ge
of a
sp
inn
ing d
isk
is
v5
r,
wh
ere
ris
th
e ra
diu
s of
th
e d
isk
an
d T
is t
he
tim
e it
tak
es t
he
poi
nt
to t
ravel
on
ce a
rou
nd
the
circ
le.
19.S
olve
the
form
ula
for
r.
r5
20.S
up
pos
e a m
erry
-go-
rou
nd
is
spin
nin
g o
nce
ever
y 3
sec
ond
s.If
a p
oin
t on
th
e ou
tsid
eed
ge
has
a s
pee
d o
f 12.5
6 f
eet
per
sec
ond
,w
hat
is t
he
rad
ius
of t
he
mer
ry-g
o-ro
un
d?
(Use
3.1
4 f
or p
.)6 f
t
Tv
} 2p
2p
}T
E } I
3 } 22 } 3
4y
21
}3
y2
5}
2
2 2
y}
5
2c
14
}3
3b
24
}2
5h
29
}r
rx1
9}
5
4 } 33 } 4
3 } 22 } 3
5 } 22 } 5
3 } 22 } 3
2p
1q
}k
2d
23c
}a
24
u1
5g
}} 9
3c
24
y}
m
2z
1y
}6
d } t
Pra
cti
ce (
Avera
ge)
So
lvin
g E
qu
ati
on
s a
nd
Fo
rmu
las
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-8
3-8
Answers (Lesson 3-8)
© Glencoe/McGraw-Hill A25 Glencoe Algebra 1
An
swers
Readin
g t
o L
earn
Math
em
ati
cs
So
lvin
g E
qu
ati
on
s a
nd
Fo
rmu
las
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-8
3-8
©G
lencoe/M
cG
raw
-Hill
183
Gle
ncoe A
lgebra
1
Lesson 3-8
Pre
-Act
ivit
yH
ow
are e
qu
ati
on
s u
sed
to
desig
n r
oll
er c
oa
ste
rs?
Rea
d t
he
intr
odu
ctio
n t
o L
esso
n 3
-8 a
t th
e to
p o
f p
age
166 i
n y
our
textb
ook
.
Th
e eq
uati
on g
(195 2
h)
5v
2co
nta
ins
sever
al
vari
able
s.W
hat
nu
mber
valu
es d
o you
kn
ow f
or t
hes
e vari
able
s in
th
is s
itu
ati
on?
32 f
or
gan
d 4
9 f
or
v
Read
ing
th
e L
ess
on
1.
Su
pp
ose
you
have
an
equ
ati
on w
ith
sev
eral
vari
able
s.Y
ou w
an
t to
sol
ve
for
a p
art
icu
lar
vari
able
.H
ow d
oes
the
pro
ced
ure
com
pare
wit
h t
hat
for
solv
ing a
n e
qu
ati
on w
ith
ju
ston
e vari
able
? H
ow d
oes
the
solu
tion
com
pare
wit
h t
he
solu
tion
for
an
equ
ati
on w
ith
on
evari
able
?
Sam
ple
an
sw
er:
Th
e p
roced
ure
is b
asic
ally t
he s
am
e.
Yo
u u
se p
rop
ert
ies
of
op
era
tio
ns a
nd
eq
uality
to
iso
late
th
e v
ari
ab
le i
n w
hic
h y
ou
are
inte
reste
d.
Th
e s
olu
tio
n w
ill
pro
bab
ly c
on
tain
vari
ab
les i
nste
ad
of
just
an
um
ber.
2.
Des
crib
e w
hat
dim
ensi
onal
an
aly
sis
invol
ves
.
Sam
ple
an
sw
er:
Yo
u u
se t
he u
nit
s a
lon
g w
ith
nu
mb
er
valu
es a
s y
ou
do
calc
ula
tio
ns.
Yo
u t
reat
the u
nit
s p
rett
y m
uch
th
e s
am
e w
ay y
ou
wo
uld
vari
ab
les.
Fo
r exam
ple
, yo
u c
an
div
ide t
hem
an
d u
se e
xp
on
en
ts w
ith
them
.
3.
Wh
at
do
you
have
to b
e ca
refu
l abou
t w
hen
you
use
vari
able
s in
den
omin
ato
rs o
ffr
act
ion
s?
Yo
u h
ave t
o b
e s
ure
th
at
yo
u d
o n
ot
use v
alu
es t
hat
wo
uld
make t
he
den
om
inato
r 0.
Help
ing
Yo
u R
em
em
ber
4.
Wh
en y
ou g
ive
the
dim
ensi
ons
of a
rec
tan
gle
,you
have
to t
ell
how
man
y u
nit
s lo
ng i
t is
an
d h
ow m
an
y u
nit
s w
ide
it i
s.H
ow c
an
th
is h
elp
you
rem
ember
wh
at
dim
ensi
onal
an
aly
sis
invol
ves
.
Sam
ple
an
sw
er:
Keep
th
e w
ord
s d
imen
sio
nan
d u
nit
in m
ind
. In
dim
en
sio
nal
an
aly
sis
, yo
u i
nclu
de u
nit
s f
or
dim
en
sio
ns i
n c
alc
ula
tio
ns.
1 } 2
©G
lencoe/M
cG
raw
-Hill
184
Gle
ncoe A
lgebra
1
Dr.
Bern
ard
o H
ou
ssay
Even
th
ough
res
earc
her
s h
ave
bee
n s
tud
yin
g t
he
dis
ease
dia
bet
esm
elli
tus
for
hu
nd
red
s of
yea
rs,sc
ien
tist
s h
ave
only
rec
entl
y d
isco
ver
edth
e ca
use
of
the
dis
ease
an
d d
evel
oped
met
hod
s fo
r re
du
cin
g i
tsse
ver
ity.
Dr.
Ber
nard
o H
ouss
ay,
an
Arg
enti
ne
ph
ysi
olog
ist,
was
one
ofth
e p
ion
eers
of
this
mor
e m
oder
n r
esea
rch
.H
e st
ud
ied
th
e re
lati
onsh
ipbet
wee
n d
iabet
es a
nd
th
e p
itu
itary
gla
nd
,an
d i
n 1
947 b
ecam
e th
e fi
rst
Lati
n A
mer
ican
to
win
th
e N
obel
Pri
ze i
n M
edic
ine
an
d P
hysi
olog
y.
Th
ough
th
ere
is n
o cu
re f
or d
iabet
es,sp
ecif
ic d
iets
an
d e
xer
cise
can
hel
pp
eop
le c
ontr
ol t
he
dis
ease
.Th
e A
mer
ican
Dia
bet
es A
ssoc
iati
on (
AD
A)
has
hel
ped
est
abli
sh f
lexib
le d
ieta
ry g
uid
elin
es f
or c
onsu
mer
s to
fol
low
.T
hes
e gu
idel
ines
in
clu
de
som
e of
th
e fo
llow
ing g
ener
al
nu
trit
ion
ru
les.
•F
at
inta
ke
shou
ld b
e eq
ual
to o
r le
ss t
han
30%
of
dail
y c
alo
ries
.
•S
atu
rate
d f
at
inta
ke
shou
ld b
e eq
ual
to o
r le
ss t
han
10%
of
dail
yca
lori
es.
•P
rote
in s
hou
ld b
e li
mit
ed t
o 10%
to
20%
of
dail
y c
alo
ries
.P
erso
ns
show
ing t
he
init
ial
sign
s of
dia
bet
es-i
nd
uce
d k
idn
ey d
isea
se s
hou
ldli
mit
pro
tein
to
10%
of
dail
y c
alo
ries
.
•C
hol
este
rol
inta
ke
shou
ld b
e 300 m
illi
gra
ms
or l
ess
dail
y.
Refe
r t
o t
he i
nfo
rm
ati
on
ab
ov
e f
or E
xercis
es 1
–4.
1.
Rob
ert
con
sum
ed 2
100 c
alo
ries
on
Tu
esd
ay.
His
fat
inta
ke
tota
led
70 g
ram
s,an
d o
f th
at
70 g
ram
s,14 w
ere
satu
rate
d.
a.
Wh
at
per
cen
tage
of h
is c
alo
rie
con
sum
pti
on w
as
fat,
an
d w
hat
per
cen
tage
of t
hat
fat
was
satu
rate
d?
(To
fin
d t
he
per
cen
tage
ofca
lori
es f
rom
fat,
mu
ltip
ly t
he
nu
mber
of
fat
gra
ms
by 9
bef
ore
div
idin
g b
y t
he
nu
mber
of
calo
ries
.) 3
0%
; 20%
b.
Did
Rob
ert
stay w
ith
in t
he
reco
mm
end
ed a
llow
an
ce o
f fa
ts?
yes
2.
An
na's
ch
oles
tero
l in
tak
e w
as
330 m
illi
gra
ms
on S
un
day.
By w
hat
per
cen
tage
doe
s sh
e n
eed
to
red
uce
her
ch
oles
tero
l co
nsu
mp
tion
to
rem
ain
wit
hin
th
e gu
idel
ines
? 10%
3.
Wh
at
nu
mber
of
fat
gra
ms
is 3
0%
of
240 c
alo
ries
? 8
4.
Sh
aro
n f
ollo
ws
a d
iet
that
pro
vid
es a
bou
t 50 g
ram
s of
pro
tein
each
day.
Sh
aro
n's
doc
tor
has
just
tol
d h
er t
o re
du
ce h
er d
ail
y p
rote
inin
tak
e by 3
0%
.A
bou
t h
ow m
uch
pro
tein
wil
l be
in h
er r
edu
ced
pro
tein
die
t?35 g
ram
s
En
rich
men
t
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D__
___
3-8
3-8
Answers (Lesson 3-8)
© Glencoe/McGraw-Hill A26 Glencoe Algebra 1
Stu
dy G
uid
e a
nd I
nte
rven
tion
Weig
hte
d A
vera
ges
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-9
3-9
©G
lencoe/M
cG
raw
-Hill
185
Gle
ncoe A
lgebra
1
Lesson 3-9
Mix
ture
Pro
ble
ms
Weig
hte
d A
vera
ge
The w
eig
hte
d a
vera
ge M
of
a s
et
of
data
is t
he s
um
of
the p
roduct
of
each n
um
ber
in
the s
et
and its
weig
ht
div
ided b
y t
he s
um
of
all
the w
eig
hts
.
Mix
ture P
ro
ble
ms
are
pro
ble
ms
wh
ere
two
or m
ore
part
s are
com
bin
ed i
nto
a w
hol
e.T
hey
invol
ve
wei
gh
ted
aver
ages
.In
a m
ixtu
re p
roble
m,th
e w
eigh
t is
usu
all
y a
pri
ce o
r a p
erce
nt
of s
omet
hin
g.
Dele
cta
ble
Co
ok
ie C
om
pa
ny
sell
s ch
oco
late
ch
ip c
oo
kie
s fo
r $
6.9
5p
er p
ou
nd
an
d w
hit
e c
ho
co
late
co
ok
ies
for $
5.9
5 p
er p
ou
nd
.H
ow
ma
ny
po
un
ds
of
ch
oco
late
ch
ip c
oo
kie
s sh
ou
ld b
e m
ixed
wit
h 4
po
un
ds
of
wh
ite c
ho
co
late
co
ok
ies
to o
bta
in a
mix
ture t
ha
t se
lls
for $
6.7
5 p
er p
ou
nd
.
Let
w5
the
nu
mber
of
pou
nd
s of
ch
ocol
ate
ch
ip c
ook
ies
Nu
mb
er
of
Po
un
ds
Pri
ce p
er
Po
un
dTo
tal
Pri
ce
Ch
oco
late
Ch
ipw
6.9
56.9
5w
Wh
ite C
ho
co
late
45
.95
4(5
.95)
Mix
ture
w1
46.7
56.7
5(w
14)
Equ
ati
on:6.9
5w
14(5
.95)
56.7
5(w
14)
Sol
ve
the
equ
ati
on.
6.9
5w
14(5
.95)
56.7
5(w
14)
Origin
al equation
6.9
5w
123.8
05
6.7
5w
127
Sim
plif
y.
6.9
5w
123.8
0 2
6.7
5w
56.7
5w
127 2
6.7
5w
Subtr
act
6.7
5w
from
each s
ide.
0.2
w1
23.8
05
27
Sim
plif
y.
0.2
w1
23.8
0 2
23.8
05
27 2
23.8
0S
ubtr
act
23.8
0 f
rom
each s
ide.
0.2
w5
3.2
Sim
plif
y.
w5
16
Sim
plif
y.
16 p
oun
ds
of c
hoc
olate
ch
ip c
ook
ies
shou
ld b
e m
ixed
wit
h 4
pou
nd
s of
wh
ite
choc
olate
coo
kie
s.
1.S
OLU
TIO
NS
How
man
y g
ram
s of
su
gar
mu
st b
e ad
ded
to
60 g
ram
s of
a s
olu
tion
th
at
is32%
su
gar
to o
bta
in a
sol
uti
on t
hat
is 5
0%
su
gar?
21.6
g
2.N
UT
ST
he
Qu
ik M
art
has
two
kin
ds
of n
uts
.P
ecan
s se
ll f
or $
1.5
5 p
er p
oun
d a
nd
waln
uts
sel
l fo
r $1.9
5 p
er p
oun
d.H
ow m
an
y p
oun
ds
of w
aln
uts
mu
st b
e ad
ded
to
15
pou
nd
s of
pec
an
s to
mak
e a m
ixtu
re t
hat
sell
s fo
r $1.7
5 p
er p
oun
d?
15 l
b
3.IN
VE
ST
ME
NT
SA
lice
Gle
aso
n i
nves
ted
a p
orti
on o
f $32,0
00 a
t 9%
in
tere
st a
nd
th
ebala
nce
at
11%
in
tere
st.H
ow m
uch
did
sh
e in
ves
t at
each
rate
if
her
tot
al
inco
me
from
bot
h i
nves
tmen
ts w
as
$3,2
00.
$16,0
00 a
t 9%
an
d $
16,0
00 a
t 11%
4.M
ILK
Wh
ole
mil
k i
s 4%
bu
tter
fat.
How
mu
ch s
kim
mil
k w
ith
0%
bu
tter
fat
shou
ld b
ead
ded
to
32 o
un
ces
of w
hol
e m
ilk
to
obta
in a
mix
ture
th
at
is 2
.5%
bu
tter
fat?
19.2
oz
Example
Example
Exercises
Exercises
©G
lencoe/M
cG
raw
-Hill
186
Gle
ncoe A
lgebra
1
Un
ifo
rm M
oti
on
Pro
ble
ms
Mot
ion
pro
ble
ms
are
an
oth
er a
pp
lica
tion
of
wei
gh
ted
aver
ages
.U
nif
orm
mo
tio
n p
ro
ble
ms
are
pro
ble
ms
wh
ere
an
obje
ct m
oves
at
a c
erta
insp
eed
,or
rate
.U
se t
he
form
ula
d5
rtto
sol
ve
thes
e p
roble
ms,
wh
ere
dis
th
e d
ista
nce
,r
isth
e ra
te,an
d t
is t
he
tim
e.
Bil
l G
uti
errez d
ro
ve a
t a
sp
eed
of
65 m
iles
per h
ou
r o
n a
nex
press
wa
y f
or 2
ho
urs.
He t
hen
dro
ve f
or 1
.5 h
ou
rs
at
a s
peed
of
45 m
iles
per
ho
ur o
n a
sta
te h
igh
wa
y.W
ha
t w
as
his
av
era
ge s
peed
?
M5
Definitio
n o
f w
eig
hte
d a
vera
ge
<56.4
Sim
plif
y.
Bil
l d
rove
at
an
aver
age
spee
d o
f abou
t 56.4
mil
es p
er h
our.
1.T
RA
VE
LM
r.A
nd
ers
an
d M
s.R
ich
each
dro
ve
hom
e fr
om a
bu
sin
ess
mee
tin
g.M
r.A
nd
ers
travel
ed e
ast
at
100 k
ilom
eter
s p
er h
our
an
d M
s.R
ich
tra
vel
ed w
est
at
80 k
ilom
eter
s p
erh
ours
.In
how
man
y h
ours
wer
e th
ey 1
00 k
ilom
eter
s ap
art
.h
2.A
IRP
LA
NE
SA
n a
irp
lan
e fl
ies
750 m
iles
du
e w
est
in 1
hou
rs a
nd
750 m
iles
du
e so
uth
in 2
hou
rs.W
hat
is t
he
aver
age
spee
d o
f th
e air
pla
ne?
ab
ou
t 429 m
ph
3.T
RA
CK
Sp
rin
ter
A r
un
s 100 m
eter
s in
15 s
econ
ds,
wh
ile
spri
nte
r B
sta
rts
1.5
sec
ond
sla
ter
an
d r
un
s 100 m
eter
s in
14 s
econ
ds.
If e
ach
of
them
ru
ns
at
a c
onst
an
t ra
te,w
ho
isfu
rth
er i
n 1
0 s
econ
ds
aft
er t
he
start
of
the
race
? E
xp
lain
.
Sp
rin
ter
A;
sin
ce s
pri
nte
r A
ru
ns 1
00 m
in
15 s
,th
is s
pri
nte
r ru
ns a
t a
rate
of
m/s
.In
10 s
eco
nd
s,sp
rin
ter
A w
ill
have r
un
(1
0)
566.7
m.
Sp
rin
ter
B’s
rate
is
.In
10 s
eco
nd
s,w
ith
th
e d
ela
yed
sta
rt,sp
rin
ter
B
has r
un
(1
0 2
1.5
) 5
60.7
m.
4.T
RA
INS
An
exp
ress
tra
in t
ravel
s 90 k
ilom
eter
s p
er h
our
from
Sm
all
vil
le t
o M
egato
wn
.A
loc
al
train
tak
es 2
.5 h
ours
lon
ger
to
travel
th
e sa
me
dis
tan
ce a
t 50 k
ilom
eter
s p
erh
our.
How
far
ap
art
are
Sm
all
vil
le a
nd
Meg
ato
wn
?281.2
5 k
m
5.C
YC
LIN
GT
wo
cycl
ists
beg
in t
ravel
ing i
n t
he
sam
e d
irec
tion
on
th
e sa
me
bik
e p
ath
.O
ne
travel
s at
15 m
iles
per
hou
r,an
d t
he
oth
er t
ravel
s at
12 m
iles
per
hou
r.W
hen
wil
l th
ecy
clis
ts b
e 10 m
iles
ap
art
?3
h
6.T
RA
INS
Tw
o tr
ain
s le
ave
Ch
icago,
one
travel
ing e
ast
at
30 m
iles
per
hou
r an
d o
ne
travel
ing w
est
at
40 m
iles
per
hou
r.W
hen
wil
l th
e tr
ain
s be
210 m
iles
ap
art
?3 h
1 } 3
100
}14
100
}14
100
}15
100
}15
1 } 2
5 } 9
65 ?
2 1
45 ?
1.5
}}
2 1
1.5
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued)
Weig
hte
d A
vera
ges
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-9
3-9 Example
Example
Exercises
Exercises
Answers (Lesson 3-9)
© Glencoe/McGraw-Hill A27 Glencoe Algebra 1
An
swers
Skil
ls P
racti
ce
Weig
hte
d A
vera
ges
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-9
3-9
©G
lencoe/M
cG
raw
-Hill
187
Gle
ncoe A
lgebra
1
Lesson 3-9
SE
AS
ON
ING
Fo
r E
xercis
es
1–4
,u
se t
he f
oll
ow
ing
in
form
ati
on
.
A h
ealt
h f
ood
sto
re s
ells
sea
son
ing b
len
ds
in b
ulk
.O
ne
ble
nd
con
tain
s 20%
basi
l.S
hei
law
an
ts t
o ad
d p
ure
basi
l to
som
e 20%
ble
nd
to
mak
e 16 o
un
ces
of h
er o
wn
30%
ble
nd
.L
et b
rep
rese
nt
the
am
oun
t of
basi
l S
hei
la s
hou
ld a
dd
to
the
20%
ble
nd
.
1.
Com
ple
te t
he
table
rep
rese
nti
ng t
he
pro
ble
m.
Ou
nces
Am
ou
nt
of
Basil
20%
Basil B
len
d16 2
b0.2
0(1
6 2
b)
100%
Basil
b1.0
0b
30%
Basil B
len
d16
0.3
0(1
6)
2.
Wri
te a
n e
qu
ati
on t
o re
pre
sen
t th
e p
roble
m.
0.2
0(1
6 2
b)
11.0
0b
50.3
0(1
6)
3.
How
man
y o
un
ces
of b
asi
l sh
ould
Sh
eila
use
to
mak
e th
e 30%
ble
nd
?2 o
z
4.
How
man
y o
un
ces
of t
he
20%
ble
nd
sh
ould
sh
e u
se?
14 o
z
HIK
ING
Fo
r E
xercis
es
5–7
,u
se t
he f
oll
ow
ing
in
form
ati
on
.
At
7:0
0 A
.M.,
two
gro
up
s of
hik
ers
beg
in 2
1 m
iles
ap
art
an
d h
ead
tow
ard
each
oth
er.T
he
firs
tgro
up
,h
ikin
g a
t an
aver
age
rate
of
1.5
mil
es p
er h
our,
carr
ies
ten
ts,sl
eep
ing b
ags,
an
dco
okin
g e
qu
ipm
ent.
Th
e se
con
d g
rou
p,h
ikin
g a
t an
aver
age
rate
of
2 m
iles
per
hou
r,ca
rrie
sfo
od a
nd
wate
r.L
et t
rep
rese
nt
the
hik
ing t
ime.
5.
Cop
y a
nd
com
ple
te t
he
table
rep
rese
nti
ng t
he
pro
ble
m.
rt
d5
rt
Fir
st
gro
up
of
hik
ers
1.5
t1.5
t
Seco
nd
gro
up
of
hik
ers
2t
2t
6.
Wri
te a
n e
qu
ati
on u
sin
g t
that
des
crib
es t
he
dis
tan
ces
travel
ed.
1.5
t1
2t
521
7.
How
lon
g w
ill
it b
e u
nti
l th
e tw
o gro
up
s of
hik
ers
mee
t?6 h
SA
LE
SF
or E
xercis
es
8 a
nd
9,
use
th
e f
oll
ow
ing
in
form
ati
on
.
Ser
gio
sel
ls a
mix
ture
of
Vir
gin
ia p
ean
uts
an
d S
pan
ish
pea
nu
ts f
or $
3.4
0 p
er p
oun
d.T
om
ak
e th
e m
ixtu
re,h
e u
ses
Vir
gin
ia p
ean
uts
th
at
cost
$3.5
0 p
er p
oun
d a
nd
Sp
an
ish
pea
nu
tsth
at
cost
$3.0
0 p
er p
oun
d.H
e m
ixes
10 p
oun
ds
at
a t
ime.
8.
How
man
y p
oun
ds
of V
irgin
ia p
ean
uts
doe
s S
ergio
use
?8 l
b
9.
How
man
y p
oun
ds
of S
pan
ish
pea
nu
ts d
oes
Ser
gio
use
?2 l
b
©G
lencoe/M
cG
raw
-Hill
188
Gle
ncoe A
lgebra
1
GR
AS
S S
EE
DF
or E
xercis
es
1–4,
use
th
e f
oll
ow
ing
in
form
ati
on
.
A n
urs
ery s
ells
Ken
tuck
y B
lue
Gra
ss s
eed
for
$5.7
5 p
er p
oun
d a
nd
Tall
Fes
cue
seed
for
$4.5
0 p
er p
oun
d.T
he
nu
rser
y s
ells
a m
ixtu
re o
f th
e tw
o k
ind
s of
see
d f
or $
5.2
5 p
er p
oun
d.
Let
kre
pre
sen
t th
e am
oun
t of
Ken
tuck
y B
lue
Gra
ss s
eed
th
e n
urs
ery u
ses
in 5
pou
nd
s of
the
mix
ture
.
1.
Com
ple
te t
he
table
rep
rese
nti
ng t
he
pro
ble
m.
Nu
mb
er
of
Po
un
ds
Pri
ce p
er
Po
un
dC
ost
Ken
tucky B
lue G
rass
k$5.7
55.7
5k
Ta
ll F
escu
e5 2
k$4.5
04.5
0(5
2k
)
Mix
ture
5$5.2
55.2
5(5
)
2.
Wri
te a
n e
qu
ati
on t
o re
pre
sen
t th
e p
roble
m.
5.7
5k
14.5
0(5
2k)
55.2
5(5
)
3.
How
mu
ch K
entu
cky B
lue
Gra
ss d
oes
the
nu
rser
y u
se i
n 5
pou
nd
s of
th
e m
ixtu
re?
3 l
b
4.
How
mu
ch T
all
Fes
cue
doe
s th
e n
urs
ery u
se i
n 5
pou
nd
s of
th
e m
ixtu
re?
2 l
b
TR
AV
EL
Fo
r E
xercis
es
5–7
,u
se t
he f
oll
ow
ing
in
form
ati
on
.
Tw
o co
mm
ute
r tr
ain
s ca
rry p
ass
enger
s bet
wee
n t
wo
citi
es,on
e tr
avel
ing e
ast
,an
d t
he
oth
erw
est,
on d
iffe
ren
t tr
ack
s.T
hei
r re
spec
tive
stati
ons
are
150 m
iles
ap
art
.B
oth
tra
ins
leave
at
the
sam
e ti
me,
one
travel
ing a
t an
aver
age
spee
d o
f 55 m
iles
per
hou
r an
d t
he
oth
er a
t an
aver
age
spee
d o
f 65 m
iles
per
hou
r.L
et t
rep
rese
nt
the
tim
e u
nti
l th
e tr
ain
s p
ass
each
oth
er.
5.
Cop
y a
nd
com
ple
te t
he
table
rep
rese
nti
ng t
he
pro
ble
m.
rt
d5
rt
Fir
st Tra
in55
t55
t
Seco
nd
Tra
in65
t65
t
6.
Wri
te a
n e
qu
ati
on u
sin
g t
that
des
crib
es t
he
dis
tan
ces
travel
ed.
55
t1
65
t5
150
7.
How
lon
g a
fter
dep
art
ing w
ill
the
train
s p
ass
each
oth
er?
1.2
5 h
8.T
RA
VE
LT
wo
train
s le
ave
Rale
igh
at
the
sam
e ti
me,
one
travel
ing n
orth
,an
d t
he
oth
erso
uth
.T
he
firs
t tr
ain
tra
vel
s at
50 m
iles
per
hou
r an
d t
he
seco
nd
at
60 m
iles
per
hou
r.In
how
man
y h
ours
wil
l th
e tr
ain
s be
275 m
iles
ap
art
?2.5
h
9.JU
ICE
A p
inea
pp
le d
rin
k c
onta
ins
15%
pin
eap
ple
ju
ice.
How
mu
ch p
ure
pin
eap
ple
ju
ice
shou
ld b
e ad
ded
to
8 q
uart
s of
th
e d
rin
k t
o ob
tain
a m
ixtu
re c
onta
inin
g 5
0%
pin
eap
ple
juic
e?5.6
qt
Pra
cti
ce (
Avera
ge)
Weig
hte
d A
vera
ges
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-9
3-9
Answers (Lesson 3-9)
© Glencoe/McGraw-Hill A28 Glencoe Algebra 1
Readin
g t
o L
earn
Math
em
ati
cs
Weig
hte
d A
vera
ges
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-9
3-9
©G
lencoe/M
cG
raw
-Hill
189
Gle
ncoe A
lgebra
1
Lesson 3-9
Pre
-Act
ivit
yH
ow
are s
co
res
ca
lcu
late
d i
n a
fig
ure s
ka
tin
g c
om
peti
tio
n?
Rea
d t
he
intr
odu
ctio
n t
o L
esso
n 3
-9 a
t th
e to
p o
f p
age
171 i
n y
our
textb
ook
.
Wh
y i
s th
e su
m o
f Il
ia K
uli
k’s
sco
res
div
ided
by 3
?
Her
firs
t sco
re i
s c
ou
nte
d o
nce a
nd
her
seco
nd
sco
re i
sco
un
ted
tw
ice
.
Read
ing
th
e L
ess
on
1.
Rea
d t
he
def
init
ion
of
wei
gh
ted
aver
age
on p
age
171 o
f you
r te
xtb
ook
.W
hat
is m
ean
t by
the
wei
gh
t of
a n
um
ber
in
a s
et o
f d
ata
?
the n
um
ber
of
tim
es t
he n
um
ber
occu
rs i
n t
he s
et
of
data
2.
Lin
da’s
qu
iz s
core
s in
sci
ence
are
90,85,85,75,85,an
d 9
0.W
hat
is t
he
wei
gh
t of
th
esc
ore
85?
3
3.
Su
pp
ose
Cli
nt
dri
ves
at
50 m
iles
per
hou
r fo
r 2 h
ours
.T
hen
he
dri
ves
at
60 m
iles
per
hou
r fo
r 3 h
ours
.
a.
Wri
te h
is s
pee
d f
or e
ach
hou
r of
th
e tr
ip.
Sp
eed
50
50
60
60
60
Ho
ur
12
34
5
b.
Wh
at
is t
he
wei
gh
t of
each
of
the
two
spee
ds?
50 m
ph
:2;
60 m
ph
:3
Help
ing
Yo
u R
em
em
ber
4.
Mak
ing a
table
can
be
hel
pfu
l in
sol
vin
g m
ixtu
re p
roble
ms.
In y
our
own
wor
ds,
exp
lain
how
you
use
a t
able
to
solv
e m
ixtu
re p
roble
ms.
Co
mp
lete
each
ro
w t
o w
rite
an
exp
ressio
n i
n t
he l
ast
co
lum
n f
or
each
part
of
the p
rob
lem
an
d f
or
the c
om
bin
ati
on
,th
en
wri
te a
n e
qu
ati
on
usin
g t
ho
se e
xp
ressio
ns f
rom
th
e l
ast
co
lum
n.
©G
lencoe/M
cG
raw
-Hill
190
Gle
ncoe A
lgebra
1
Dio
ph
an
tin
e E
qu
ati
on
s
Th
e fi
rst
gre
at
alg
ebra
ist,
Dio
ph
an
tus
of A
lexan
dri
a (
abou
t A.D
.300),
dev
oted
mu
ch o
f h
is w
ork
to
the
solv
ing o
f in
det
erm
inate
equ
ati
ons.
An
in
det
erm
inate
equ
ati
on h
as
mor
e th
an
on
e vari
able
an
d a
nu
nli
mit
ed n
um
ber
of
solu
tion
s.A
n e
xam
ple
is
x1
2y
54.
Wh
en t
he
coef
fici
ents
of
an
in
det
erm
inate
equ
ati
on a
re i
nte
ger
s an
dyou
are
ask
ed t
o fi
nd
sol
uti
ons
that
mu
st b
e in
teger
s,th
e eq
uati
on i
sca
lled
dio
ph
an
tin
e.S
uch
equ
ati
ons
can
be
qu
ite
dif
ficu
lt t
o so
lve,
oft
en
in
volv
ing t
rial
an
d e
rror—
an
d s
om
e l
uck
!
So
lve e
ach
dio
ph
an
tin
e e
qu
ati
on
by
fin
din
g a
t le
ast
on
e p
air
of
po
siti
ve
inte
gers
tha
t m
ak
es
the e
qu
ati
on
tru
e.
So
me h
ints
are g
iven
to
help
yo
u.
1.
2x
15y
532
a.
Fir
st s
olv
e t
he e
qu
ati
on
for
x.
x5
16 2
b.
Wh
y m
ust
ybe a
n e
ven
nu
mber?
If y
is o
dd
,th
en
xw
on
’t b
e a
n i
nte
ger.
c.
Fin
d a
t le
ast
on
e s
olu
tion
.A
ny o
f th
ese:
(11,2),
(6,4),
(1,6)
2.
5x
12y
542
a.
Fir
st s
olv
e t
he e
qu
ati
on
for
x.
x5
b.
Rew
rite
you
r an
swer
in t
he f
orm
x5
8 1
som
e e
xp
ress
ion
.x
58 1
c.
Wh
y m
ust
(2 2
2y)
be a
mu
ltip
le o
f 5?
Oth
erw
ise
,x
wo
n’t
be a
n i
nte
ger.
d.
Fin
d a
t le
ast
on
e s
olu
tion
.A
ny o
f th
ese:
(8,1),
(6,6),
(4,11),
(2,16)
3.
2x
17y
529
4.
7x
15y
5118
(11,1)
or
(4,3)
An
y o
f th
ese:
(14,4),
(9,11),
(4,18)
5.
8x
213y 5
100
6.
3x
14y
522
(19,4),
(32,12)
or
an
y p
air
(6,1)
or
(2,4)
wh
en
y5
4n
an
d n
is a
p
osit
ive o
dd
nu
mb
er
7.
5x
214
y5
11
8.
7x
13y
540
(5,1),
(19,6)
or
an
y p
air
(4
,4)
or
(1,11)
wh
en
y5
5m
24 a
nd
mis
a p
osit
ive n
um
ber
2 2
2y
}5
42 2
2y
}5
5y
}2
En
rich
men
t
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
3-9
3-9
Answers (Lesson 3-9)
![[3] Compl Probl](https://static.fdocuments.in/doc/165x107/55cf8df5550346703b8d1701/3-compl-probl.jpg)
