SOLUTION: One number is three times another. The sum of their reciprocals is four over nine. Find the numbers.

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Question 314188: One number is three times another. The sum of their reciprocals is four over nine. Find the numbers.
Found 2 solutions by Fombitz, ankor@dixie-net.com:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let A and B be the numbers.
A=3B
1%2FA%2B1%2FB=4%2F9
From eq. 1,
1%2F3B%2B1%2FB=4%2F9
1%2F3B%2B3%2F%283B%29=4%2F9
%284%2F%283B%29%29=4%2F9
highlight%28B=3%29
Then from the first equation,
A=3B
highlight%28A=9%29

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
One number is three times another.
x = 3y
:
The sum of their reciprocals is four over nine.
1%2Fx + 1%2Fy = 4%2F9
:
Find the numbers.
Replace x with (3y)
1%2F%283y%29 + 1%2Fy = 4%2F9
multiply each term by 9y, results
3 + 9 = 4y
12 = 4y
y = 12%2F4
y = 3
find x
x = 3(3)
x = 9
:
:
Check solution
1%2F9 + 1%2F3 = 4%2F9
1%2F9 + 3%2F9 = 4%2F9
: