SOLUTION: one number is 10 times larger than another. the difference of their reciprocal is 1. what are the 2 numbers?

Question 339269: one number is 10 times larger than another. the difference of their reciprocal is 1. what are the 2 numbers?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
one number is 10 times larger than another. the difference of their reciprocal is 1. what are the 2 numbers?
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Let the numbers be x and y.
Equations:
x = y + 10
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1/x - 1/y = 1
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Substitute for "x" and solve for "y":
1/(y+10) - (1/y) = 1
Multiply thru by y(y+10) to get:
y - (y+10) = y(y+10)
10 = y^2+10y
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y^2+10y-10 = 0
y = [-10 +- sqrt(100-4*-10)]/2
y = [-10 +- sqrt(140)]/2
y = [-10 +-2sqrt(35)]/2
y = [-5 +- sqrt(35)]
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Substitute for "y" and solve for "x":
x = y+10
x = 5+-sqrt(35)
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Cheers,
Stan H.
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