Question 201243: The sum of two numbers is 13 and the differene of the reciprocals of the numbers is 3/40. Determine the two numbers. Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website! The sum of two numbers is 13 and the differene of the reciprocals of the numbers is 3/40. Determine the two numbers.
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A big clue is the 40, that's the product, so they're 5 and 8.
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x+y = 13
1/x - 1/y = 3/40
(y - x)/xy = 3/40
40*(y-x) = 3xy
Sub y = 13-x
40(13-x) - 40x = 3x*(13-x)
-80x + 520 = 39x - 3x^2
3x^2 - 119x + 520 = 0
(x - 5)*(3x - 104) = 0
x = 5
y = 8
