PSAT Math Multiple-Choice Question 134: Answer and Explanation

Question: 134

Sam's Sunscreen Shop makes two kinds of sunscreen: Sunscreen A and Sunscreen B. Sunscreen A contains 8% of the active ingredient, and Sunscreen B has 12.5% of the same active ingredient. Sam wants to create a new sunscreen by blending the two sunscreens to make a new product that has a concentration of more than 10% active ingredient. The sunscreen should be in a tube containing at least 12 ounces, but no more than 16 ounces. If a represents the ounces of Sunscreen A in the blend and b represents the ounces of Sunscreen B in the blend, which of the following systems can be used to solve for all the values of a and b that fit these requirements?

• A.
• B.
• C.
• D.

Correct Answer: D

Explanation:

D

The question asks for a system of inequalities that models a specific situation. Translate the information in Bite-Sized Pieces and eliminate after each piece. One piece of information says that the tube must contain at least 12 ounces, but no more than 16 ounces. Because the amount in the tube is a + b, the answer should contain 12 ≤ a + b ≤ 16. Eliminate (A) and (B) which do not include this inequality. Compare the remaining answer choices. The difference between (C) and (D) is the third inequality: specifically, whether 0.10 should be multiplied by (a + b). The question states that the product should have a concentration of more than 10% active ingredient. The active ingredient should be more than 10 percent of the total product, so the correct answer must multiply 0.10 by the total product. Eliminate (C) which does not multiply 0.10 by any other term. The correct answer is (D).