Digital PSAT Math Practice Question 235: Answer and Explanation

Question: 235

An animal shelter can house only cats and dogs. Each dog requires 2 cups of food and three treats a day, while each cat requires 1 cup of food a day and 2 treats a day. If the shelter has 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, you come up with an expression to represent the amount of food consumed. Each dog consumes 2 cups, so d dogs will consume 2d cups of food. Each cat consumes 1 cup of food, so c cats will consume c cups of food. Together, the dogs and cats consume 2d + c cups of food. The shelter has 400 cups of food, so 2d + c cannot exceed 400. This can be represented by the inequality 2d + c ≤ 400.

Similarly, each dog needs 3 treats daily, so d dogs eat 3d treats. Cats eat 2 treats daily, so c cats need 2c treats daily. The shelter has 500 treats, so 3d + 2c cannot exceed 500:

3d + 2c ≤ 500. These two equations match answer (B).