SOLUTION: Suppose that the sum of two whole numbers is 10, and the sum of their reciprocals is 5/8. Find the numbers.

Question 737004: Suppose that the sum of two whole numbers is 10, and the sum of their reciprocals is 5/8. Find the numbers.
Answer by unlockmath(1688) (Show Source): You can put this solution on YOUR website!
Hello,
Good problem.
Let x and y be the numbers.
x+y=10
1/x+1/y=5/8
Let's use substitution.
x=10-y Now plug it into the second equation.
1/(10-y)+1/y=5/8
Multiply by 8y(10-y) to get:
8y+8(10-y)=5y(10-y)
Expand:
8y+80-8y=50y-5y^2
Set to zero:
5y^2-50y+80=0
Factor:
(y-2)(5y-40)
y=2 or y=8
Therefore we know the numbers are
x=2
y=8
Make sense?
RJ
www.math-unlock.com
RJ
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