SOLUTION: Positive integers x and y have a product of 56 and x < y. Seven times the reciprocal of the smaller integer plus 14 times the reciprocal of the larger integer equals 4. What is the

Question 921289: Positive integers x and y have a product of 56 and x < y. Seven times the reciprocal of the smaller integer plus 14 times the reciprocal of the larger integer equals 4. What is the value of x?
Answer by CubeyThePenguin(3113) (Show Source): You can put this solution on YOUR website!
xy = 56
7(1/x) + 14(1/y) = 4

Simplify the second equation.
7/x + 14/y = 4
(7y + 14x)/(xy) = 4
7y + 14x = 4 * 56 = 224 ----> 2x + y = 32 ---> y = 32 - 2x

Substitute this into the first equation.

xy = 56
x(32 - 2x) = 56
-2x^2 + 32x - 56 = 0
x^2 - 16x + 28 = 0
(x - 2)(x - 14) = 0

x is the smaller integer, so x = 2 and y = 28.
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