SOLUTION: The sum of two numbers is 20. The sum of their reciprocals is 4/15. Find the two numbers AND One number is 8 more than another number. The sum of their reciprocals is 1/3. Fi

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Question 989235: The sum of two numbers is 20. The sum of their reciprocals is 4/15. Find the two numbers
AND
One number is 8 more than another number. The sum of their reciprocals is 1/3. Find the two numbers.
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
The sum of two numbers is 20. The sum of their reciprocals is 4/15.
Find the two numbers
x + y = 20
1/x + 1/y = 4/15
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Substitute for "x" and solve for "y"::
1/(20-y) + 1/y = 4/15
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15y + 15(20-y) = 4y(20-y)
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15*20 = 80y - 4y^2
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y^2 -20y +75 = 0
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y = 15 or y = 5
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If y = 15, x = 5
If y = 5, x = 15
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AND
One number is 8 more than another number. The sum of their reciprocals is 1/3. Find the two numbers.
x - y = 8
1/x + 1/y = 1/3
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Same procedure as with the 1st problem.
Substitute for "x" and solve for "y"::
etc.
Cheers,
Stan H.
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Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Cross-multiply, collect like terms, and solve the resulting quadratic for . The two roots will be the values of x and y that you need.

AND

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John

My calculator said it, I believe it, that settles it