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Question 502500: Suppose that the sum of two whole numbers is 6, and the sum of their reciprocals is 3/4. Find the numbers.
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! Suppose that the sum of two whole numbers is 6, and the sum of their reciprocals is 3/4. Find the numbers.
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Let the two numbers be x and y
Given:
x + y = 6
1/x + 1/y = 3/4
Use the first equation to solve for y: y = 6 - x
Substitute this value in the 2nd equation:
1/x + 1/(6-x) = 3/4
Collect like terms:
((6-x) + x)/(x(6-x)) = 3/4
6/(x(6-x)) = 3/4
This simplifies to x^2 - 6x + 8 = 0
Factor:
(x-2)(x-4) = 0
If we choose x = 2 -> y = 4
If we choose x = 4 -> y = 2
Either way, the numbers are 2 and 4
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