Table of ContentsTopic Page #...3.4B Many or No Solution 333.8A Solving Equations 353.8B Solving Formulas 376.5 Absolute Value Equations 393.5/3.6 Ratios and Proportions 41

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3.5/3.6 Ratios and Proportions

Ratio:Relation between 2 numbers

a:b ab a to b

You always have to write ratios in the simplest form.

You never write the answer as a mixed fraction

Ex 1: Cell phoneA person makes 6 long distance calls and 15 local calls in 1 month.

a. Find the ratio of long distance calls to local calls.

615

= 25

Ex 1: Cell phoneA person makes 6 long distance calls and 15 local calls in 1 month.

b. Find the ratio of local calls to long distance calls

156

= 52

Ex 1: Cell phoneA person makes 6 long distance calls and 15 local calls in 1 month.

c. Find the ratio of long distance calls to all calls.

621

= 27

Ex 2: SportsA volleyball team plays 14 home matches and 10 away matches.

a. Find the ratio of home matches to away matches.

1410

= 75

Ex 2: SportsA volleyball team plays 14 home matches and 10 away matches.

b. Find the ratio of home matches to all matches.

1424

= 712

Ex 2: SportsA volleyball team plays 14 home matches and 10 away matches.

c. Find the ratio of away matches to all matches.

1024

= 512

Proportions:When two ratios are equal

a cb d

(bd) (bd)

ad = bc

Cross multiplya cb d

ad = bc

Ex #3: Solve.

109 6k

6k = 906 6k = 15

34

x12

4x = 364 4

x = 9

Ex #3: Solve.

34

x12

1 3

x = 9

Reduce around the box

34

x12

4x = 364 4

x = 9

58 24

t

8t = 120

t = 15

58 24

t

1 3

t = 15

y3

31

y = 9

1 33 y

y = 9

863

xx

3(x + 8) = 6x

8 = x

3x + 24 = 6x24 = 3x

3 68x x

x = 8

1 2

2x = x + 8

812

24

xx

24(x – 12) = 8x

18 = x

24x – 288 = 8x–288 = –16x

1224 8x x

x = 18

3 13x – 36 = x2x – 36 = 0

2x = 36

Ex #4: ArchitectAn architect creates a scale model of a school. The school is 50 feet high. The ratio of the model to the actual school is 1 foot to 75 feet. Estimate the height of the model.

modelactual 50

h 1

75

50h

175

2 3

3h = 2

h = 23

Ex #5:A map has a scale factor of 1cm : 15km. If the distance of the map is 6cm, find the actual distance.

115

6x

x = 90

Ex #6:Write the sentence as a proportion and solve.

3 is to 8 as is to 32x

38

32x

1 4

x = 12

Ex #6:Write the sentence as a proportion and solve.

x is to 4 as 8 is to 16

4x

8161 4

x = 21

2