BTGModeratorVI wrote: ↑Sun Aug 02, 2020 6:56 am
In a certain animal shelter, the ratio of the number of dogs to the number of cats is 15 to 7. If 12 additional cats were to be taken in by the shelter, the ratio of the number of dogs to the number of cats would be 15 to 11. How many dogs are in the shelter?
A. 15
B. 25
C. 30
D. 45
E. 60
Answer:
D
Source: Veritas Prep
Here's a solution that involves two variables
In a certain animal shelter, the ratio of the number of dogs to the number of cats is 15 to 7
Let D = number of dogs in shelter
Let C = number of cats in shelter
We can write: D/C = 15/7
Cross multiply to get: 7D = 15C
Rewrite as:
15C - 7D = 0
If 12 additional cats were to be taken in by the shelter, the ratio of the number of dogs to the number of cats would be 15 to 11
So, C + 12 = RESULTING number of cats in the shelter
We can write: D/(C + 12) = 15/11
Cross multiply to get: 11D = 15(C + 12)
Expand right side to get: 11D = 15C + 180
Rewrite as:
12C - 11D = -180
How many dogs are in the shelter?
We have the following system:
15C - 7D = 0
12C - 11D = -180
Subtract the bottom equation from the top equation to get: 4D = 180
Solve: D = 45
Answer: D
Cheers,
Brent
