There are 20 percent fewer dogs than cats and all together there are 171 dogs and cats. How many dogs do I have and how many cats do I have?

Question

I need an equation  

Answer 1

Let x = # cats and y = # dogs and set up a system of 2 equations in 2 variables:

 

y= x-20  and x + y = 171  and solve via substitution:

 

x + (x-20) = 171

 

2x = 191

 

x = 95.5, it is impossible to have 1/2 of a cat, so check to make sure your numbers in the problem are correct

Answer 2

d = c -20 (20 fewer d than c)

c + d = 171 (total pets)

 

Now plug in and solve.

 

c + (c-20) = 171

2c - 20 = 171

2c = 191

c = 95.5

 

Since you can't have a half cat, either round up or down. In this case, we'll round up to 96.

 

d = 96 - 20 = 76

 

Since we rounded up on the cats, then we need to round down on the dogs to adjust for the 171 total (because 96+76=172).  So the answer is 96 cats, 75 dogs.