John want to build a rectangular puppy kennel up against his house. The side against the house doesn't need a fence, so John still need to build 3 fences. He got 31 feet of fence. the fence parallel to the side against the house should be 15 feet long. So he still need to determine the side of the 2 other fences, which are equal because its a rectangular (the parallel sides in a rectangular are equal).
So the equation that models the situation is:
31 = 2s + 15, in which s represents the length of the one fence.
We need to solve for s. Let's subtract 15 from each side to have the variables on a side and the numbers on the other:
31 = 2s + 15
31 - 15 = 2s + 15 - 15
16 = 2s
Then divide both sides by 2 to have the variable s on a side and its value on the other:
16 = 2s
16/2 = (2s)/2
8 = s.
So the shorter sides of the rectangle needs to be 8 feet long each.
Let's check our answer:
2s + 15 = 16 + 15 = 31.
Our answer has been approved.
Hope this helps! :D