Solve by factoring... Word Problems.

Question

I have a test tomorrow on how to solve by factoring, but the catch is that they are word problems. Can you help me solve one of these equations? Here is one... ( Please explain as much as possible, because I am highly confused.)

A 50 m by 120 m park consists of a rectangular lawn surrounded by a path of uniform width. Find the dimensions of the lawn if its area is the same as the area of the path. Let X = the width of path.

Answer 1

Draw and label a diagram!!!

A_park = (50)(120)

A_lawn = (50 - 2x)(120 - 2x)

A_path = (50)(120) - (50 - 2x)(120 - 2x)

A_awn = A_path

(50 - 2x)(120 - 2x) = (50)(12) - (50 - 2x)(120- 2x)

Can you solve for x and answer?