SOLUTION: Devide 27 into two part such that the sum of their reciprocalis 3/20.

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Question 1061661: Devide 27 into two part such that the sum of their reciprocalis 3/20.

Answer by josgarithmetic(39795) About Me  (Show Source):
You can put this solution on YOUR website!
system%28x%2By=27%2C1%2Fx%2B1%2Fy=3%2F20%29

y%2Bx=%283%2F20%29xy
20y%2B20x=3xy


y=27-x
substitute into the fraction equation.
20%2827-x%29%2B20x=3x%2827-x%29
540-20x%2B20x=81x-3x%5E2
540=81x-3x%5E2
180=27x-x%5E2
-x%5E2%2B27x-180=0
x%5E2-27x%2B180=0 which is factorable.
%28x-12%29%28x-15%29=0
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system%28x=12%2COR%2Cx=15%29.

The two numbers are 12 and 15.