SOLUTION: One number is three times another. The sum of their reciprocals is 2/3. What are the numbers?

Algebra ->  Finance -> SOLUTION: One number is three times another. The sum of their reciprocals is 2/3. What are the numbers?       Log On


   

Question 1185374: One number is three times another. The sum of their reciprocals is 2/3. What are the numbers?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
x and 3x, the numbers

1%2Fx%2B1%2F%283x%29=2%2F3
3%2F%283x%29%2B1%2F%283x%29=2%2F3
4%2F%283x%29=2%2F3
4%2Fx=2
highlight%28x=2%29

The numbers are 2 and 6.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

One number is three times another. The sum of their reciprocals is 2/3. What are the numbers?
Let smaller number be S

Then larger is 3S

We then get: matrix%281%2C3%2C+1%2FS+%2B+1%2F%283S%29%2C+%22=%22%2C+2%2F3%29

3 + 1 = 2S ------- Multiplying by LCD, 3S

4 = 2S

Smaller number, or highlight_green%28matrix%281%2C5%2C+S%2C+%22=%22%2C+4%2F2%2C+%22=%22%2C+2%29%29

It's now quite easy to find the larger number.