Question

There are a total of 165 dogs and cats waiting for homes at the Grand Strand Humane Society. The number of cats is 24 less than twice the number of dogs.

Part A: Identify both variables you are using, then write equations to represent both situations
Part B: How many dogs and cats are waiting to be adopted in the shelter? You must show work. Write your answer in the form of a sentence

Answer 1

Part A

Let d = number of dogs

Let c = number of cats

Given:

• total of 165 dogs and cats

⇒ d + c = 165

Given:

• The number of cats is 24 less than twice the number of dogs

⇒ c = 2d - 24

Part B

Substitute c = 2d - 24 into d + c = 165 and solve for d:

⇒ d + 2d - 24 = 165

⇒ 3d - 24 = 165

⇒ 3d = 189

⇒ d = 63

Substitute found value of d into d + c = 165 and solve for c:

⇒ 63 + c = 165

⇒ c = 102

Therefore, 63 dogs and 102 cats are adopted in the shelter.