SOLUTION: One number is 3 times another. If the sum of their reciprocals is 2/9 , find the two numbers

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Question 984261: One number is 3 times another. If the sum of their reciprocals is 2/9 , find the two numbers
Found 2 solutions by solver91311, jim_thompson5910:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!




Solve for , then calculate

John

My calculator said it, I believe it, that settles it

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!


One number is 3 times another. which means y+=+3x


If the sum of their reciprocals is 2/9, then 1%2Fx+%2B+1%2Fy+=+2%2F9


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1%2Fx+%2B+1%2Fy+=+2%2F9


1%2Fx+%2B+1%2F%283x%29+=+2%2F9 Replace y with 3x (works because y = 3x)


9x%281%2Fx+%2B+1%2F%283x%29%29+=+9x%282%2F9%29 Multiply both sides by the LCD 9x to clear out the fractions.


9x%281%2Fx%29+%2B+9x%281%2F%283x%29%29+=+9x%282%2F9%29


9+%2B+3+=+2x


12+=+2x


12%2F2+=+x


x+=+6


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y+=+3x


y+=+3%286%29 Plug in x = 6


y+=+18


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The two numbers are 6 and 18.