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

Algebra ->  Sequences-and-series -> SOLUTION: One number is 3 times another. The sum of their reciprocals is 16/3. Find the numbers.      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
4 and 12
1/4 and 3/4

--

Numbers, x and 3x
1%2Fx%2B1%2F%283x%29=16%2F3
3%2F%283x%29%2B1%2F%283x%29=16%2F3
4%2F%283x%29=16%2F3
1%2F3x=4%2F3
3x=3%2F4
highlight_green%28x=1%2F4%29
highlight%28%29,...

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

One number is x, the other number is 3x.


The equation is

    1%2Fx + 1%2F%283x%29 = 16%2F3.


Multiply both sides by 3x. You will get then


    3 + 1 = 16x

    4 = 16x

    x = 4%2F16 = 1%2F4.


ANSWER.  The numbers are 1%2F4  and 3%2F4.


CHECK.   The reciprocal numbers are 4 and 4%2F3, and their sum is  4 + 4%2F3 = %2812%2B4%29%2F3 = 16%2F3.  ! Precisely correct. !

Solved.

---------------

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


Answer by MathTherapy(10552) About Me  (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: matrix%281%2C3%2C+1%2FS+%2B+1%2F%283S%29%2C+%22=%22%2C+16%2F3%29

3 + 1 = 16S ------ Multiplying by LCD, 3S

4 = 16S



The numbers are NOT 4 & 12.

Answer by greenestamps(13200) About Me  (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.