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

Question 805594: Jackie mows a strip of uniform width around her 25 m by 15 m rectangular lawn and leaves a patch of lawn that is 60% of the original area. What is the width of the strip?
Found 2 solutions by ankor@dixie-net.com, josgarithmetic:
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 15 m rectangular lawn and leaves a patch of lawn that is 60% of the original area.
What is the width of the strip?
:
Let x = the width of the strip
:
Find the total area: 25*15 = 375 sq/m
then .6(375) = 225 sq/m is the remaining 60%
:
A uniform strip x, around the lawn, subtracts 2x from the original dimensions
(25-2x)*(15-2x) = 225
FOIL
375 - 50x - 30x + 4x^2 = 225
Combine like terms to form a quadratic equation
4x^2 - 80x + 375 - 225 = 0
4x^2 - 80x + 150 = 0
simplify, divide by 2
2x^2 - 40x + 75 = 0
unfortunately this will not factor, using the quadratic formula

I got two solutions, approx:
x = 17.9
and
x = 2.1m is the reasonable value for x
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Original area, 25*15 square meters.
60% of original area, (0.6)(25)(15).
Let x = width of the strip around the unmowed area.

One side of the unmowed rectangle is 25-2x meters.
The other side of the unmowed rectangle is 15-2x meters.

Area of unmowed region is

If you do not feel like checking for factorability, use general solution:

meters

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