Question

Kendrenks kennel has 2 spots for cats for every 7 spots for dogs if he has a total og 144 spots for both cats and dogs then how many more spots does he have for dogs than cats

Answer 1

Kendrenks kennel has 80 more spots for dogs than spots for cats

Explanation:

Hi

First of all we are going to define the unknowns of the problem, so
`x` number of spots for cats and
`y` number of spots for dogs. Then as the problem has two unknowns, we have to build two equations to solve it.

Using "if he has a total of 144 spots for both cats and dogs" we have one, so

`(1) \ x+y=144`

Then "Kendrenks kennel has 2 spots for cats for every 7 spots for dogs", the other one
`(2) \ x=(2y)/(7)`.

Replace (2) in (1) we get
`(2y)/(7) +y=144`, multiplying both sides by 7
`2y+7y=1008\\9y=1008\\y=(1008)/(9) =112\ Dogs\ Spots`, then this info in (2)
`x=(2y)/(7)=(2(112))/(7)=(224)/(7)=32\ Cats\ Spots`.

Finally as the question is "how many more spots does he have for dogs than cats?" , the answer is
`y-x=112-32=80`