Question

Olivia is a volunteer at the animal shelter. The animal shelter has only dogs and cats. 1/3 of the animals are dogs. There are 16 fewer dogs than cats. How many animals are there in the animal shelter?

a. 48
b. 64
c. 72
d. 96

Answer 1

By setting up equations based on the given proportions and differences between the numbers of dogs and cats, we solve for the total number of animals in the shelter to be 48.

Step-by-step explanation:

Olivia volunteered at the animal shelter, which housed only dogs and cats. It's stated that 1/3 of the animals are dogs, and there are 16 fewer dogs than cats. We can approach this problem by setting up equations. Let's denote the total number of animals as T, the number of dogs as D, and the number of cats as C. We know:

• D = 1/3 * T (since 1/3 of the animals are dogs)
• C = D + 16 (since there are 16 fewer dogs than cats)

Substituting the first equation into the second gives us:

1. C = (1/3 * T) + 16
2. We also know that all the animals are either dogs or cats, so T = D + C
3. Replacing D with 1/3*T from the first equation, we get T = 1/3*T + C
4. To solve for C, we rearrange the equation to 2/3*T = C
5. Using the second bullet point, we can replace C in this equation to get 2/3*T = 1/3*T + 16
6. Solving for T, we find that T = 48

So, the correct answer is 48 animals in the animal shelter.