How to Find the Ratio of Cats and Dogs in a Shelter on the SAT

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Problem

In April of 2004, d dogs and c cats lived in an animal shelter. If 4 cats arrived at the shelter in May of 2004 and the ratio of dogs to cats remained unchanged, in terms of c and d, how many dogs arrived at the shelter in May of 2004? 
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​(A) 4
(B) 4d/c
(C) d/c
(D) d^2 - 4d
(E) (2cd + 4d)/c

Solution

12. B

​The original ratio of dogs to cats was d/c. 4 cats arrived, giving a total of c + 4 cats. You don’t know how many dogs arrived, so call that number x, producing a total of d + x dogs. The ratio remains unchanged, so set the new ratio of dogs to cats equal to the original ratio: 

(d + x)/(c + 4) = d/c
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Cross-multiply: c(d + x) = d(c + 4) 
Distribute: cd + cx = cd + 4d 
Subtract cd: cx = 4d 
Divide by c: x = 4d/c 

Answer, x = 4d/c.