algebra word problem

Question

A rectangle is five times as long as it is wide. If it were 24 cm shorter and 24 cm wider, it would be a square. What are its dimensions?

Answer 1

L=5W

L-24 = W +24

5W -24 = W+24

4W = 48

W = 48/4 =12

L=5W =5(12) = 60

It's a 12x60 rectangle

12+24 = 60-24

36 = 36

Answer 2

We use the variable w to represent the width.

We use the variable z to represent the length(l is a horrible letter to use a variable) and we know:

"five times as long as it is wide"

or in an equation:

z = 5w

Squares have equal sides. Or in other words, the width and length are equal. What do we need to do to the current dimensions to make them equal?

"24 cm shorter"

means we need to subtract 24 from the length. Thus, (z - 24) will be the square's side.

"24 cm wider"

means we need to add 24 to the width. Thus, (w + 24) will also be the square's side.

These must be equal so our second equation is

z - 24 = w + 24

Thus, we need to solve the system

z = 5w

z - 24 = w + 24

I would recommend the substitution method.