Ch 8: ExponentsG) Mixture Word Problems

Objective:

To solve mixture word problems.

+

4 oz

=

6 oz

25% solution 50% solution

10 oz

1/4 3/6 4/1040% solution

Illustration

Size % Total

Item A

Item B

Mixture

Rules1) Set up a table (see below) and insert given data

2) Multiply across to determine the Total for each row

3) Add down to calculate the Mixture row

4) Solve the equation from the Mixture row

×

×+ +

×

9 oz. of mixed nuts containing 40% peanuts were mixed with 6 oz. of another kind of mixed nuts that contain 65% peanuts. Peanuts are what percent of the new mixture?

Size % Total

Mixed Nuts 1

Mixed Nuts 2

Mixture

9 oz .40

6 oz .65

x

×

×

3.603.90

+ +

15 oz 7.5 oz

15 7.5x =15 15

x = .50 = 50%

Example 1

4 yd3 of soil containing 15% sand was mixed into 6 yd3 of soil containing 50% sand. What is the sand content of the mixture?

Size % Total

Solution 1

Solution 2

Mixture

4 yd3 .15

6 yd3 .50

x

×

×

.603.00

+ +

10 yd3 3.60

10 3.6x =10 10

x = .36 = 36%

Classwork 1

9 lb of Abhasra's special coffee blend was made by combining 3 lb of brand X coffee which costs $24/lb with 6 lb of brand Y coffee which costs $18/lb. Find the cost per lb of the mixture.

Size Cost Total

Brand X

Brand Y

Mixture

3 lb $24/lb

6 lb $18/lb

x

×

×

$72$108

+ +

9 lb $180

9 180x =9 9

x = $20/lb

Example 2

Matt mixed together 2 liters of Brand A fruit punch and 3 liters of Brand B. Brand A contains 25% fruit juice and Brand B contains 30% fruit juice. What percent of the mixture is fruit juice?

Size % Total

Brand A

Brand B

Mixture

2 L .25

3 L .30

x

×

×

.50

.90+ +

5 L 1.40

5 1.4x =5 5

x = .28 = 28%

Classwork 2

12 L of a 70% alcohol solution was mixed with 6 L of a 10% alcohol solution. What is the concentration of the mixture?

Size % Total

Solution 1

Solution 2

Mixture

12 L .70

6 L .10

x

×

×

8.40.60

+ +

18 L 9.00

18 9x =18 18

x = .50 = 50%

Classwork 3

How many ml of an 88% alcohol solution must be mixed with 10 ml of pure water to make an 8% solution?

Size %Alcohol

Water

Mixture

x .88

10 ml 0

.08

×

×

.88x0

+ +

10 + x .88x(10 + x) .88x(.08)=

.8 .8

x = 10 ml

8 + .08x = .88x-.08x -.08x

8 = .8x

Total

Example 3

How much of Brand A fruit punch (25% fruit juice) must be mixed with 10 gal. of Brand B fruit punch (55% fruit juice) to create a mixture containing 40% fruit juice?

Size %Brand A

Brand B

Mixture

x .25

10 gal .55

.40

×

×

.25x5.5

+ +

10 + x 5.5 + .25x(10 + x) 5.5 + .25x(.40)=

.15 .15

x = 10 gal

4 + .40x

Total

= 5.5 + .25x-4 -4-.25x -.25x

.15x = 1.5

Classwork 4

How many lb of soybean oil which costs $4/lb must be added to 10 lb of canola oil which costs $1/lb to make vegetable oil which costs $2/lb?

Size Cost Total

Soybean Oil

Canola Oil

Mixture

x $4/lb

10 lb $1/lb

$2/lb

×

×

4x10

+ +

10 + x 10 + 4x

Classwork 5

(10 + x) 10 + 4x(2) =

2 2

x = 5 lb

20 + 2x = 10 + 4x-10 -10

10 = 2x

-2x -2x

Kayla created a metal containing 25% iron by combining two other metals. One of these metals weighed 1 mg and contained 70% iron. The other weighed 3 mg. How much iron did it contain? Size %

Metal 1

Metal 2

Mixture

1 mg .70

3 mg x

.25

×

×

.73x

+ +

4 mg .7 + 3x(4) .7 + 3x(.25)=

3 3

x = .10

1.00

Total

= .7 + 3x-.7 -.7

.3 = 3x

Classwork 6

= 10%