PSAT Math Grid-Ins Question 10: Answer and Explanation

Question: 10

Kimberly is an apiologist studying the sugar content of different sugar-water solutions to determine which is preferred by her hive of honeybees. After trying Solution 1, which has a sugar content of 25%, and Solution 2, which has a sugar content of 10%, she decides to make a new solution. She mixes 50 ounces of Solution 1 with some quantity of Solution 2 to make Solution 3, which has a sugar content of 15%. How many ounces of Solution 2 did Kimberly use to make Solution 3?

Correct Answer: 100

Explanation:

100

The question asks for the number of ounces of Solution 2 used to make Solution 3. Use Bite-Sized Pieces to write an equation. Solution 3 is composed of 50 ounces of Solution 1 and x ounces of Solution 2. Solution 1 has a sugar content of 25%, and Solution 2 has a sugar content of 10%. Apply those sugar contents to the amounts of Solution 1 and Solution 2 in Solution 3 to get 0.25(50) + 0.10x. Solution 3 has a sugar content of 15%; since Solution 3 is made up of 50 ounces of Solution 1 and x ounces of Solution 2, the expression 0.15(50 + x) represents Solution 3. Set the two expressions equal to each other to solve for x. 0.25(50) + 0.10x = 0.15(50 + x). Distribute the numbers in front of the parentheses to get 12.5 + 0.10x = 7.5 + 0.15x. Subtract 7.5 from both sides to get 5 + 0.1x = 0.15x. Subtract 0.1x from both sides to get 5 = 0.05x. Divide both sides by 0.05 to get x = 100. The correct answer is 100.