Question

How do I solve:
Find two numbers whose sum is 25 and the sum of whose reciprocals is 1/6.

Can anyone help me with this problem?

So far I have, x + y = 25 and 1/x + 1/y =1/6

Answer 1

what do you mean by thro ?

Answer 2

x+y=25, so x = 25 -y
1/x + 1/y = 1/6

From the second equation, you get
(y+x)/xy = 1/6
6x + 6y = xy

Substitute x into the equation,
6(25 -y) + 6y = y(25 -y)
150 - 6y + 6y = 25 y - y^2
y^2 - 25 y + 150 = 0
(y -10) (y-15) = 0

therefore y =10 or 15, and x = 15 or 10
(sorry about before)

Answer 3

No problem, thank you so much! I'm awful at math.