Lesson 3.9- Weighted Averages, pg. 171

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Lesson 3.9- Weighted Averages, pg. 171 Goals: To solve mixture problems. To solve uniform motion problems.

Vocabulary Weighted average: the sum of the product of the number of units and the value of units and the value per unit divided by the sum of the number of units. Mixture problems: problems in which two or more parts are combined into a whole.

Ex. 1: Pets Jeri likes to feed her cat gourmet cat food that costs $1.75 per pound. However, food at that price is too expensive so she combines it with cheaper cat food that costs $0.50 per pound. How many pounds of cheaper food should Jeri buy to go with 5 pounds of gourmet food, if she wants the average price to be $1.00 per pound?

Auto Maintenance To provide protection against freezing, a car’s radiator should contain a solution of 50% antifreeze. Darryl has 2 gallons of a 35% antifreeze solution. How many gallons of 100% antifreeze solution should Darryl add to his solution to produce a solution of 50% antifreeze?

FOOD How many quarts of pure orange juice should Michael add to a 10% orange drink to create 6 quarts of a 40% orange juice mixture? Let p represent the number of quarts of pure orange juice he should add to the orange drink.

Business Cookies Inc. sells peanut butter cookies for $6.50 per dozen and chocolate chip cookies for $9.00 per dozen. Yesterday, they sold 85 dozen more peanut butter cookies than chocolate chip cookies. The total sales for both types of cookies were $4055.50. Let p represent the number of dozens of peanut butter cookies sold.

METALS In 2000, the international price of gold was $270 per ounce, and the international price of silver was $5 per ounce. Suppose gold and silver were mixed to obtain 15 ounces of an alloy worth $164 per ounce. Let g represent the amount of gold used in the alloy.