SOLUTION: Jackie mows a strip of uniform width around her 25m by 15m rectangular lawn and leaves a patch of lawn that is 60% of the original area. What is the width of the strip?

Click here to see ALL problems on Miscellaneous Word Problems

Question 123447: Jackie mows a strip of uniform width around her 25m by 15m rectangular lawn and leaves a patch of lawn that is 60% of the original area. What is the width of the strip?
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
Jackie mows a strip of uniform width around her 25 m by 15m rectangular lawn and leaves a patch of lawn that is 60% of the original area. What is the width of the strip?
:
Draw this as one rectangle inside another rectangle. Label the large rectangle
as 25 by 15. Label the width of the strip between the rectangle as x. I will be
apparent that the dimension of the inner rectangle will be (25-2x) by (15-2x)
:
Find the area of whole lawn: 25 * 15 = 375 sq/m
:
It said the inner area was 60% of the whole lawn: .6 * 375 = 225 sq/m
:
An equation of the inner area would be:
(25-2x)*(15-2x) = 225
FOIL
375 - 50x - 30x + 4x^2 = 225
Arrange as a quadratic equation:
4x^2 - 80x + 375 - 225 = 0
:
4x^2 - 80x + 150 = 0
:
Use the quadratic equation to solve this: a=4; b=-80; c=150

:

Find the square root of 4000
Two solutions

x = 17.9
and

x = 2.1, this the solution that makes sense
:
The width of the mown strip is 2.1 meters
:
:
Check solution by finding the area of the inner portion
2x = 2*2.1 = 4.2
(25-4.2) * 15-4.2) =
20.8 * 10.8 = 224.64 ~ 225 which is 60% of 375