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?
(D) d^2 - 4d
(E) (2cd + 4d)/c
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
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.
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