Acertain pet store has only cats and dogs. the ratio of the number of cats to the number of dogs in the pet store is 2: 3.  14  of the cats and  12  of the dogs wear collars. if 48 animals wear collars, what is the total number of animals in the pet store?

First we define variables:
 x = number of cats
 y = number of dogs
 We now write the system of equations:
 x / y = 2/3
 (1/4) x + (1/2) y = 48
 Solving the system we have:
 x = 48
 y = 72
 The total number of animals is:
 x + y = 48 + 72 = 120
 
 The total number of animals in the pet store is:
 120 animals