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Question 150507: the length and width of a rectangle are in the ratio 3:2. if the length is increased by 20 and the width is decreased by 5, the ratio of the length to the width becomes 2:1. find the length and width of this rectangle.
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! the length and width of a rectangle are in the ratio 3:2. if the length is increased by 20 and the width is decreased by 5, the ratio of the length to the width becomes 2:1. find the length and width of this rectangle.
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Let x = length
and y = width
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since we have two unknowns, we need two equations.
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From: "the length and width of a rectangle are in the ratio 3:2." we get equation 1:
x/y = 3/2
or
2x = 3y (equation 1)
.
From: "if the length is increased by 20 and the width is decreased by 5, the ratio of the length to the width becomes 2:1" we get equation 2:
(x+20)/(y-5) = 2/1
or
(x+20) = 2(y-5) (equation 2)
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Let's solve equation 1 for x:
2x = 3y
x = (3/2)y
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Substitute the above into equation 2 and solve for y:
(x+20) = 2(y-5)
((3/2)y+20) = 2(y-5)
multiplying both sides by 2:
(3y+40) = 4(y-5)
3y + 40 = 4y - 20
60 = y
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Finally, substitute the above into equation 1 and solve for x:
2x = 3y
2x = 3(60)
2x = 180
x = 90
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length = 90
width = 60
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