SOLUTION: One number is 3 times another. If the sum of their reciprocals Is 1/6, find the two numbers.

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Question 107477: One number is 3 times another. If the sum of their reciprocals
Is 1/6, find the two numbers.
Found 2 solutions by alisttutors, jim_thompson5910:
Answer by alisttutors(8) About Me  (Show Source):
You can put this solution on YOUR website!
Let the numbers be A and B
A=3B
1/A+1/B=1/6 or A+B=6 (taking the reciprocal of both sides)
Substitute the first equation into the second:
3B+B=6
4B=6 therefore B=3/2 or 1 1/2
A would therefore equal 9/2 or 4 1/2

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=first number, y=second number

Since one number (say the first number) is 3 times the other, then

x=3y

Now the statement "..the sum of their reciprocals
Is 1/6" translates to:

1%2Fx%2B1%2Fy=1%2F6


1%2F%283y%29%2B1%2Fy=1%2F6 Now plug in x=3y


1%2F%283y%29%2B%281%2Fy%29%283%2F3%29=1%2F6 Now multiply the second fraction by 3%2F3 to get to the common denominator 3y


1%2F%283y%29%2B%283%29%2F%283y%29=1%2F6 Multiply


%281%2B3%29%2F%283y%29=1%2F6 Combine the fractions


4%2F%283y%29=1%2F6 Combine the numerators



4=%283y%29%2F6 Multiply both sides by 3y


24=3y Multiply both sides by 6


8=y Divide both sides by 3 to solve for y


So one number is 8


Now multiply 8 by 3 to find the first number

x=3%2A8=24


So another number is 24



Answer:

So our answer is
x=8 and y=24



Check:

Remember their reciprocals should add to 1%2F6


1%2F8%2B1%2F24 Turn 8 into 1/8 and 24 into 1/24


=3%2F24%2B1%2F24 Multiply 1/8 by 3/3



=4%2F24 Add the fractions


=1%2F6 Reduce



So our answer is verified


note: the previous answer is incorrect. When you check by adding the reciprocal of 3/2 and 9/2 you get 2%2F3%2B2%2F9=6%2F9%2B2%2F9=8%2F9 which is not 1%2F6