SOLUTION: One number is 3 times another. The sum of their reciprocals is 16/3. Find the numbers.

Question 1156495: One number is 3 times another. The sum of their reciprocals is
16/3. Find the numbers.
Found 4 solutions by josgarithmetic, ikleyn, MathTherapy, greenestamps:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
~~4 and 12~~
1/4 and 3/4

--

Numbers, x and 3x

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Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.

One number is x, the other number is 3x. The equation is + = . Multiply both sides by 3x. You will get then 3 + 1 = 16x 4 = 16x x = = . ANSWER. The numbers are and . CHECK. The reciprocal numbers are 4 and , and their sum is 4 + = = . ! Precisely correct. !

Solved.

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Ignore the post by @josgaritnmetic, since it is   T O T A L L Y   W R O N G.

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

One number is 3 times another. The sum of their reciprocals is
16/3. Find the numbers.

Let the smaller number be S
Then the larger number is 3S
We then get:
3 + 1 = 16S ------ Multiplying by LCD, 3S
4 = 16S

The numbers are NOT 4 & 12.
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

If the two numbers are in the ratio 3:1, then their reciprocals are in the ratio 1:3.

So divide the given sum of the reciprocals, 16/3, into two parts in the ratio 1:3. Those two parts are 4/3 and 12/3=4.

Since the reciprocals are 4/3 and 4, the two numbers are 3/4 and 1/4.

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