PSAT Math Multiple-Choice Question 795: Answer and Explanation

Question: 795

An animal shelter can house only cats and dogs. Each dog requires 2 cups of food and 3 treats a day, while each cat requires 1 cup of food a day and 2 treats a day. If the shelter has available a total of 400 cups of food and 500 treats a day, what expressions portray the full scope of the number of c cats and d dogs the shelter could potentially house?

• A. 2d - c ≤ 400 and 3d + c < 500
• B. 2d + c ≤ 400 and 3d + 2c ≤ 500
• C. 4d + c < 400 and d + c < 500
• D. 2d + 2c ≤ 400 and 2d + 3c ≤ 500

Correct Answer: B

Explanation:

(B) First, let's come up with an expression to represent the amount of food consumed each day. Each dog consumes 2 cups, so d dogs consume 2d cups of food daily. Each cat consumes 1 cup of food per day, so c cats will consume c cups of food daily. Together, the dogs and cats consume 2d + c cups of food every day. The shelter has 400 cups of food, so 2d + c cannot exceed 400. This can be represented by the following inequality:
2d + c ≤ 400
Similarly, each dog needs 3 treats daily, so d dogs eat 3d treats each day. Cats eat 2 treats daily, so c cats need 2c treats daily. The shelter has 500 treats available every day, so
3d + 2c cannot exceed 500:
3d + 2c ≤ 500
These two equations match choice (B).