A certain animal shelter has 28 cats and 46 dogs. How many dogs must be adopted and taken away from the animal shelter

BTGmoderatorDC wrote: ↑

Tue Mar 07, 2023 11:08 pm

A certain animal shelter has 28 cats and 46 dogs. How many dogs must be adopted and taken away from the animal shelter so that 70 percent of the animals in the shelter will be cats?

A) 6

B) 12

C) 28

D) 34

E) 40


OA D

Source: Veritas Prep

There are a total of 28 + 46 = 74 animals. Let d denote the number of dogs to be removed so that 70% of the remaining animals are cats. We can create the equation:

28/(74 - d) = 7/10

280 = 7(74 - d)

280 = 518- 7d

7d = 238

d = 34

Alternate solution:

If the cats are 70% of the animals in the shelter and since the number of cats is 28, then the total number of animals in the shelter can only be 28/0.7 = 280/7 = 40. Thus there can be only 40 - 28 = 12 dogs in the shelter. Since there are currently 46 dogs, 46 - 12 = 34 dogs should be removed.

Answer: D