SOLUTION: A positive integer is 5 less than another. If the sum of the reciprocal of the smaller and twice the reciprocal of the larger is 7/30 what is the smaller integer?
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Question 942056: A positive integer is 5 less than another. If the sum of the reciprocal of the smaller and twice the reciprocal of the larger is 7/30 what is the smaller integer?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A positive integer is 5 less than another. If the sum of the reciprocal of the smaller and twice the reciprocal of the larger is 7/30 what is the smaller integer?
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Equations::
x = y-5
Note: x is the smaller; y is the larger
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(1/x)+(2/y) = (7/30)
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Substitute for "y" and solve for "x"::
(1/x) + (2/(x+5)) = 7/30
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Multiply thru by 30x(x+5) to get:
30(x+5) + 60(x) = 7x(x+5)
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90x + 150 = 7x^2 + 35x
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7x^2 - 55x - 150 = 0
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Ans:: x = 10
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Cheers,
Stan H.
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