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

Answer:

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

Step-by-step 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 $(2) \ x=\frac{2y}{7}$.

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

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