SOLUTION: Suppose that the sum of two whole numbers is 20, and the sum of their reciprocals is 5/16. Find the numbers.
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-> SOLUTION: Suppose that the sum of two whole numbers is 20, and the sum of their reciprocals is 5/16. Find the numbers.
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Question 567777: Suppose that the sum of two whole numbers is 20, and the sum of their reciprocals is 5/16. Find the numbers. Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! Suppose that the sum of two whole numbers is 20, and the sum of their reciprocals is 5/16. Find the numbers.
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Equations:
x + y = 20
1/x + 1/y = 5/16
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x + y = 20
(x+y)/xy = 5/16
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20/xy = 5/16
5xy = 320
xy = 64
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Remember x + y = 20
x = 20-y
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Substitute:
(20-y)y = 64
20y-y^2 = 64
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y^2-20y+64 = 0
y^2-16y-4y+64 = 0
y(y-16)-4(y-16) = 0
(y-16)(y-4) = 0
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If y = 4; x = 16
If y = 16; x = 4
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Cheers,
Stan H.
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