SOLUTION: one number is 3 times another. the sum of their reciprocals is 20/3. find the numbers

Question 641184: one number is 3 times another. the sum of their reciprocals is 20/3. find the numbers
Answer by josh_jordan(263) (Show Source): You can put this solution on YOUR website!
To solve, let's turn the sentences into equations. The first sentence says that one number is 3 times another. In other words:
x = 3y
The next sentence says that the sum of their reciprocals is 20/3. In other words:

To solve, we need to substitute x in the second equation, with 3y, that way we will get rid of x and solve for y:

Next, multiply the equation by 3y. This will get rid of our fractions and leave us with:
=

Divide both sides of the equation by 20, and this will leave us with y, which will be one of our numbers:
=
So, 1/5 is one of our numbers.
We know that the other number is 3 times y. So, 3 x 1/5 will give us our other number:
3 x 1/5 = 3/5
FINAL ANSWER: 1/5 and 3/5 are the numbers
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