PSAT Math Multiple-Choice Question 112: Answer and Explanation

Question: 112

A baker has $75 with which to purchase ingredients. The baker needs to buy at least 2 containers of flour and at least 3 containers of cocoa powder. Flour costs $3.99 per container, and cocoa powder costs $5.99 per container. If f represents the number of containers of flour and c represents the number of containers of cocoa powder, which of the following systems of inequalities models this situation?

• A.
• B.
• C.
• D.

Correct Answer: C

Explanation:

C

The question asks for a system of inequalities that models a specific situation. Translate the question in Bite-Sized Pieces and eliminate after each piece. One piece of information says that the baker needs to buy at least 2 containers of flour. Since f represents the number of containers of flour, one inequality should say f ≥ 2, so eliminate (B) and (D), where this does not appear. Compare the remaining answers. The difference between (A) and (C) is the direction of the inequality sign. The question states that the baker has $75 dollars with which to purchase ingredients. Since the baker cannot spend more than this amount, the inequality should say that the total cost is ≤ 75. This does not appear in (A), so eliminate it. The correct answer is (C).