Question 105854: quadratic equations-word problem
Chris cuts half a rectangular lawn, 40m by 30m, by mowing strips around the perimeter. Jerri cuts the small rectangle left. How wide a strip does Chris cut so that they share the work equally?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Chris cuts half a rectangular lawn, 40m by 30m, by mowing strips around the perimeter. Jerri cuts the small rectangle left. How wide a strip does Chris cut so that they share the work equally?
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FInd the total area of the lawn
40 * 30 = 1200 sq/m
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Half of the lawn would be 600 sq/m (obviously)
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Let the width of strip = x
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The equation using the dimensions of the small rectangle left:
(40-2x)*(30-2x) = 600
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FOIL
1200 - 140x + 4x^2 = 600
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Arrange as a quadratic equation:
4x^2 - 140x + 1200 - 600 = 0
4x^2 - 140x + 600 = 0
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Simplify, divide by 4. (Makes it easier to factor)
x^2 - 35x + 150 = 0
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Factors to:
(x-30)(x-5) = 0
Two solutions:
x = +30, does not make sense, ignore this one
and
x = +5 ft is our solution
:
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Check our solution: find the area of half the lawn
(40-10)*(30-10) = 600
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Did this help make some sense of this for you?
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