Warm Up

#1

#2

A chemist wants to create a 28% acid solution for an experiment by adding pure acid to a 20% acid solution. If he needs 20 liters of the mixture for his experiment, how many liters of each solution must he combine?

Jim says to Tina, “if you give me $18, then I’d have exactly five times as much money as you.” Tina replies, “Why that’s not fair. I think you should give me $6 then we’d have the same amount of money.” How much money does Jim have to start with?

Warm Up#1 A chemist wants to create a 28% acid solution for an experiment by

adding pure acid to a 20% acid solution. If he needs 20 liters of the mixture for his experiment, how many liters of each solution must he combine?a = amount of 100% acid

b = amount of 20% acid solution0.28(20) = 5.6

Amount of Solution

acid

a b 20

1.00a 0.20b 5.6

+ =100%solution

20%solution

28%solution

a b 20

1.00a 0.20b 5.6

Warm Up#1 A chemist wants to create a 28% acid solution for an experiment by

adding pure acid to a 20% acid solution. If he needs 20 liters of the mixture for his experiment, how many liters of each solution must he combine?

a b 20

1.00a 0.20b 5.6

a = amount of 100% acid

b = amount of 20% acid solution

10a 2b 56

2a 2b 40

8a 16a 2

2 liters of pure acid

18 liters of 20% acid solution

Warm Up#2 Jim says to Tina, “if you give me $18, then I’d have exactly five times as much

money as you.” Tina replies, “Why that’s not fair. I think you should give me $6, then we’d have the same amount of money.” How much money does Jim have to start with?

J = Jim’s money

T = Tina’s money

Define variables:

Write two equations

E1

E2

J 18

First exchange

T 18 5 T 18 J 6

Second exchange

T 6

J 18 5T 90

J 5T 108

J 5T 108

J T 12

J T 12

J J5T 108 T 12

4T 120T 30

J im has $42

Word Problems

#3 If you decrease the denominator of a fraction by four, the new fraction that is equal to 1/2. If you subtract one from the numerator of the original fraction, then the resulting fraction would be 1/3. What is the product of the original numerator and denominator?

2n 4 d n = Numerator

d = Denominator

Define variables: Write two equations

E1

E2

nd

12

2n d 4

nd 4

2n 4 d

Homework

#3

n = Numerator

d = Denominator

Define variables: Write two equations

Homework

E1

E2

nd

13

3 n 1 d

n 1d

3n 3 d

3n 3 d d d

2n 4 3n 3 7 n

18 d

2n 4 d

126

If you decrease the denominator of a fraction by four, the new fraction that is equal to 1/2. If you subtract one from the numerator of the original fraction, then the resulting fraction would be 1/3. What is the product of the original numerator and denominator?

Homework

#6 Five years ago, Beth was three times as old as Frank. Next year she will be twice as old as Frank. How old is Beth today?

B = Beth’s age

F = Frank’s age

Define variables:

Write two equations

E1

E2

B 5

5 years ago

F 5 3 F 5 B 1

Next year

F 1 2 F 1B 5 3F 15

B 3F 10

B 3F 10

B 1 2F 2

B 2F 1

B 2F 1 B B

3F 10 2F 1 F 11

Beth is 23 years old

Homework

A rectangle has a perimeter of 18 inches. A new rectangle is formed by doubling the width and tripling the length. The new rectangle has a perimeter of 46 inches. Find the area of the new rectangle.

L = Length

W = Width

Define variables: Write two equations

2120 inches

#7

L

W

E1

E2

2L 10

2L 2W 18

3L

2WArea?

6L 4W 46 4L 4W 36 6L 4W 46

L 5W 4

15

8

#8

a = amount of pure O.J.

b = amount of 32% O.J.0.15(2) = 0.3

Amount of Solution

O.J.

a 2 b

1.00a 0.3 0.32b

+ =100%solution

15%solution

32%solution

a 2 b

1.00a 0.3 0.32b

Homework

A two-gallon mixture of fruit juice is comprised 15% orange juice. Michelle wants a fruit juice mixture to be 32% orange juice. How much pure orange juice should she add to the mixture?

#8 A two-gallon mixture of fruit juice is comprised 15% orange juice. Michelle wants a fruit juice mixture to be 32% orange juice. How much pure orange juice should she add to the mixture?

a 2 b

1.00a 0.3 0.32b

Homework

100a 30 32b

E1 E2

100a 30 a 232 100a 30 32a 64

68a 34

34a

680.5 gallons of pure O.J . 1

2

a = amount of 100% O.J.

b = amount of 32% O.J.

Word Problems

5

21

126

718

6

4.8

23

120

0.5

Word Problems

Homework Sadie works at the China Emporium packing dishes for shipments. She receives 12 cents for each piece she packs successfully and is fined 18 cents for each piece she breaks. If she handles 188 pieces and is paid $20.16, how many pieces does she break?

p = number packedb = number broken

Define variables: Write two equations

E1

E2

#1

p b 188 12p 18b 2016

12p 12b 2256 12p 18b 2016

30b 240

b 8She broke 8 dishes

HomeworkTraveling against the wind, a plane flies 2,100 miles from Chicago to San Diego in 4 hours and 40 minutes. The return trip, flying with a wind that is blowing twice as fast, takes four hours. Find the rate of the plane in still air.

To ChicagoWith the wind

2100

Rate Time Distance To S.D.

Against the wind

4p 2w p 2w 4 2100

14p w 21003

21002

43

p w

w = speed of wind (to S.D.)

p = speed of the plane

#2

Homework

#2 Traveling against the wind, a plane flies 2,100 miles from Chicago to San Diego in 4 hours and 40 minutes. The return trip, flying with a wind that is blowing twice as fast, takes four hours. Find the rate of the plane in still air.

p 2w 4 2100

14p w 21003

p w 450

p 2w 525

2p 2w 900

p 2w 525

3p 1425

p 475Plane : 475 m.p.h

w = speed of wind (to S.D.)

p = speed of the plane

Homework

#3 One number is two-thirds of another number. If the larger number is increased by 9 it becomes twice as large as the smaller number. Find the product of the two numbers.

2S L

3

L = Larger number

S = Smaller number

Define variables:

Write two equations

E1

E2 L 9 2S

3S 2L

L 2S 9

E2 E1

3S 92 2S

3S 4S 18

18 S27 L ASQ

486

Homework

#4 A store received $823 from the sale of 5 iPods and 7 video games. The receipts from the iPods exceeded receipts from the video games by $137. What is the cost of a video game?

p = cost of an iPod

v = cost of a video game

Define variables: Write two equations

E1

E2

5p 7v 823 5p 7v 137 5p 7v 137

5p 7v 823

10p 960p 96

E1

5 7v 296 8 3 480 7v 823

7v 343v 49

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