Ask a Teacher

Search



The sum of two numbers is 8. Determine the numbers if the sum of their reciprocals is 8/15.
x + y = 8
(1/x) + (1/y) = 8/15

Two equations, two unknowns. Using substitution, since y = 8 - x,

(1/x) + (1/[8 - x]) = 8/15

Multiply both sides by 15x(8 - x),

15(8 - x) + 15x = 8x(8 - x)

120 - 15x + 15x = 64x - 8x2

Move everything to the left hand side,

8x2 - 64x + 120 = 0

Divide everything by 8,

x2 - 8x + 15 = 0

And factor.

(x - 5)(x - 3) = 0

This means x = 5 or x = 3.
When x = 5, y = 3.
When x = 3, y = 5.

Your two numbers are 3 and 5.


comments powered by Disqus