PSAT Math Multiple-Choice Question 631: Answer and Explanation

Question: 631

In an animal shelter consisting of only dogs and cats, the ratio of dogs to cats is 3 to 1. If there are 360 animals in the shelter, how many dogs must be present?

• A. 90
• B. 120
• C. 270
• D. 300

Correct Answer: C

Explanation:

(C) Let's use the variable d to represent the number of dogs in the shelter and the variable c to represent the number of cats. If the ratio of dogs to cats is 3:1, then there are 3 times as many dogs as cats:

d = 3c

If there are 360 animals in the shelter:

d + c = 360

We want to know the number of dogs present. So let's solve the first equation for c in terms of d and plug this into the second equation. Dividing by 3 tells us:

Plugging this into the second equation results in:

Combining like terms gives:

We can divide both sides by (in other words, multiply both sides by ) to learn that d = 270, which is answer choice (C).

Alternatively, you can solve this as a ratio problem:

As a fraction of the whole, the number of dogs can be expressed as of the total. Then take of the total number of animals to find the number of dogs:

× 360 = 270