1. ## Elimination by Addition Method / Word Problem

I'm working on this section in my Algebra book called Elimination by Addition Method/Systems using two linear equations and I'm stuck on this word problem.
Thanks.

Suppose that we have a rectangular book cover. If the width is increased by 2 centimeters, and the length is decreased by 1 centimeter, then the area is increased by 28 square centimeters. However, if the width is decreased by 1 centimeter and the length is increased by 2 centimeters, then the area is increased by 10 square centimeters. Find the dimensions of the book cover.

This is what I tried doing

(W+2)(L-1)= 28
(W-1)(L+2)=10

I know I'm doing something wrong and I cant figure out another way to set up the equations.

2. ## Re: Elimination by Addition Method / Word Problem

Originally Posted by dcarranza
Suppose that we have a rectangular book cover. If the width is increased by 2 centimeters, and the length is decreased by 1 centimeter, then the area is increased by 28 square centimeters. However, if the width is decreased by 1 centimeter and the length is increased by 2 centimeters, then the area is increased by 10 square centimeters. Find the dimensions of the book cover.

This is what I tried doing

(W+2)(L-1)= 28
(W-1)(L+2)=10
You're showing the increases of 28 and 10 as new areas;
they really are increases to the original area of WL; so :
(W + 2)(L - 1) = WL + 28 [1]
(W - 1)(L + 2) = WL + 10 [2]

Now expand the left sides:
WL - W + 2L - 2 = WL + 28 [1]
WL + 2W - L - 2 = WL + 10 [2]

Simplify:
-W + 2L = 30 [1]
2W - L = 12 [2]

I'll leave you the satisfaction of finishing that up

3. ## Re: Elimination by Addition Method / Word Problem

I finally solved it! Thank you so much!