MATH110 American Military University Systems of Equation Word Problems

A flat rectangular piece of aluminum has a perimeter of 70 inches. The length is 11 inches longer than the width. Find the width. Why can’t I get 12, instead I keep getting 13 as the answer. What am I missing?

My work: The equation would now be, L² + 2W = P, or 22 + 2w = 70.

To isolate the W, I subtracted 22 from each side, leaving the equation with 2w divided by 48 =24. (70- 22 = 48÷2 = 24)

After this we divided the left over 24 by 2, since the width will have 2-sides, resulting in 12.

To verify the answer, plug the new variables into the equation:

2L + 2W- L = 70, or, (2L)24 + (2w)24 + (L)22= 48