Ch 8: Exponents G) Mixture Word Problems Objective: To solve mixture word problems.

Illustration + = 10 oz 6 oz 4 oz 25% solution 50% solution 1/4 3/6 4/10

Rules 1) Set up a table (see below) and insert given data Total Size % Item A × + + Item B × Mixture × 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

Example 1 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? Total Size % Mixed Nuts 1 9 oz × .40 3.60 + + Mixed Nuts 2 6 oz .65 3.90 × Mixture 15 oz x 7.5 oz 15 x = 7.5 15 15 x = .50 = 50%

Classwork 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? Total Size % Solution 1 4 yd3 × .15 .60 + + Solution 2 6 yd3 .50 3.00 × Mixture 10 yd3 x 3.60 10 x = 3.6 10 10 x = .36 = 36%

Example 2 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. Total Size Cost Brand X 3 lb × $24/lb $72 + + Brand Y 6 lb $18/lb $108 × Mixture 9 lb x $180 9 x = 180 9 9 x = $20/lb

Classwork 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? Total Size % Brand A 2 L × .25 .50 + + Brand B 3 L .30 .90 × Mixture 5 L x 1.40 5 x = 1.4 5 5 x = .28 = 28%

Classwork 3 12 L of a 70% alcohol solution was mixed with 6 L of a 10% alcohol solution. What is the concentration of the mixture? Total Size % Solution 1 12 L × .70 8.40 + + Solution 2 6 L .10 .60 × Mixture 18 L x 9.00 18 x = 9 18 18 x = .50 = 50%

Example 3 How many ml of an 88% alcohol solution must be mixed with 10 ml of pure water to make an 8% solution? Total Size % Alcohol x × .88 .88x + + Water 10 ml × Mixture 10 + x .08 .88x (10 + x) (.08) = .88x 8 = .8x 8 + .08x = .88x .8 .8 -.08x -.08x x = 10 ml

Classwork 4 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? Total Size % Brand A x × .25 .25x + + Brand B 10 gal .55 5.5 × Mixture 10 + x .40 5.5 + .25x (10 + x) (.40) = 5.5 + .25x .15x = 1.5 4 + .40x = 5.5 + .25x .15 .15 -4 -.25x -4 -.25x x = 10 gal

Classwork 5 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? Total Size Cost Soybean Oil x × $4/lb 4x + + Canola Oil 10 lb $1/lb 10 × Mixture 10 + x $2/lb 10 + 4x (10 + x) (2) = 10 + 4x 10 = 2x 20 + 2x = 10 + 4x 2 2 -10 -2x -10 -2x x = 5 lb

Classwork 6 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? Total Size % Metal 1 1 mg × .70 .7 + + Metal 2 3 mg x 3x × Mixture 4 mg .25 .7 + 3x (4) (.25) = .7 + 3x .3 = 3x 1.00 = .7 + 3x 3 3 -.7 -.7 x = .10 = 10%