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

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) (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) (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

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

Now plug in

Now multiply the second fraction by to get to the common denominator

Multiply

Combine the fractions

Combine the numerators

Multiply both sides by 3y

Multiply both sides by 6

Divide both sides by 3 to solve for y

So one number is 8

Now multiply 8 by 3 to find the first number

So another number is 24

Answer:

So our answer is
and

Check:

Remember their reciprocals should add to

Turn 8 into 1/8 and 24 into 1/24

= Multiply 1/8 by 3/3

= Add the fractions

= 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 which is not

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