Question 1166231: A man mows his 40 foot by 50 foot rectangular lawn in a spiral pattern starting from the outside edge. After a bit of hard work he stops for a water break he is 90% done. How wide of a strip has he mowed around the outside edge?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A man mows his 40 foot by 50 foot rectangular lawn in a spiral pattern starting from the outside edge.
After a bit of hard work he stops for a water break he is 90% done.
How wide of a strip has he mowed around the outside edge?
:
find the total area of the lawn: 40 * 50 = 2000 sq/ft
Find the area of the 10% that remains to be mowed, after 90% is mowed\
.10 * 2000 = 200 sq/ft
:
let x = the width of the mowed strip
(40-2x)(50-2x) = 200
FOIL
2000 - 80x - 100x + 4x^2 = 200
Arrange as a quadratic equation
4x^2 - 180x + 2000 - 200 = 0
4x^2 - 180x + 1800 = 0
simplify, divide by 4
x^2 - 45x + 450 = 0
(x-15)(x-30) = 0
Two solutions
x = 15 and x = 30 but only x=15 is reasonable (if x=30, 2x would = 60)
The width of the mowed strip = 15 ft
:
:
Check this; find the area of the unmowed lawn
(40-30)*(50-30) = 200
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