SOLUTION: I need help figuring this out - PLEASE :) One number is 5 times another. If the sum of their reciprocals is 1/5, find the two numbers. Write an equation that represents the pr

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Question 77098: I need help figuring this out - PLEASE :)
One number is 5 times another. If the sum of their reciprocals is 1/5, find the two numbers. Write an equation that represents the problem and solve.
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=one number ------------------1%2Fx will be its reciprocal
Then 5x=the other number-------------1%2F5x will be its reciprocal
Now we are told that the sum of their reciprocals equals 1%2F5. So our equation to solve is:
1%2Fx%2B1%2F5x=1%2F5 multiply both sides by 5x to get rid of the fractions
%285x%2Fx%29%2B%285x%2F5x%29=%285x%2F5%29 or
5%2B1=x and
x=6----------------------------------one number
5x=5%2A6=30---------------------------the other number
ck
30 is 5*6
also
1%2F6%2B1%2F30=1%2F5 (note that 1%2F6 is 5%2F30)
5%2F30%2B1%2F30=1%2F5
6%2F30=1%2F5
1%2F5=1%2F5


Hope this helps---ptaylor