SOLUTION: Suppose that the sum of two whole numbers is 20, and the sum of their reciprocals is 5/16. Find the numbers.

Question 567777: Suppose that the sum of two whole numbers is 20, and the sum of their reciprocals is 5/16. Find the numbers.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Suppose that the sum of two whole numbers is 20, and the sum of their reciprocals is 5/16. Find the numbers.
----------------------
Equations:
x + y = 20
1/x + 1/y = 5/16
-----------
x + y = 20
(x+y)/xy = 5/16
-----
20/xy = 5/16
5xy = 320
xy = 64
--
Remember x + y = 20
x = 20-y
---
Substitute:
(20-y)y = 64
20y-y^2 = 64
---------------
y^2-20y+64 = 0
y^2-16y-4y+64 = 0
y(y-16)-4(y-16) = 0
(y-16)(y-4) = 0
---
If y = 4; x = 16
If y = 16; x = 4
=======================
Cheers,
Stan H.
RELATED QUESTIONS
Suppose that the sum of two whole numbers is 10, and the sum of their reciprocals is 5/8. (answered by unlockmath)

suppose that the sum of two whole numbers is 11 and the sum of their reciprocals is... (answered by richard1234)

Suppose that the sum of two whole numbers is 15, and the sum of their reciprocals is... (answered by MathLover1)

Suppose that the sum of two whole numbers is 6, and the sum of their reciprocals is 3/4.... (answered by htmentor)

Suppose that the sum of two whole numbers is 9 and the sum of their reciprocals is 1/2.... (answered by jim_thompson5910)

the sum of 2 whole numbers is 9 and the sum of their reciprocals is 1/2. find the... (answered by lwsshak3)

Two numbers have a sum of 5, and the sum of their reciprocals is 1. Find the exact... (answered by josgarithmetic)

The sum of two numbers is 20. The sum of their reciprocals is 4/15. Find the two numbers (answered by stanbon,solver91311)

Suppose that the sum of two numbers is 16, and the sum of their squares is 178. Find the... (answered by meetkisai)