Algebra word problem

Question

if the side of a square is doubled and then increased by 7, the new perimeter is 8 more than 3 times the old perimeter. What is the side length of the original square? 

Answer 1

Let s = the length of the side of the square

Let p = the old perimeter = 4s

 

Let s2 = the new length of the side = 2s + 7

let p2 = the new perimeter = 4(2s + 7) = 8s + 28

 

We are given that p2 = 8 + 3*p

 

We can now substitute our values in to solve for s:

 

8s + 28 = 8 + 3(4s)

8s + 28 = 8 + 12s

28 = 8 + 4s

20 = 4s

5 = s

 

Therefore, the original length of the side was 5