SOLUTION: A fraction is such that if 5 is added to the numerator and 9 to the denominator, the value of the fraction becomes one third of the numerator of the original is doubled and the den

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Question 1039645: A fraction is such that if 5 is added to the numerator and 9 to the denominator, the value of the fraction becomes one third of the numerator of the original is doubled and the denominator is increased by 9 the resulting fraction is half. find the number
Found 2 solutions by ankor@dixie-net.com, MathTherapy:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Rewrote the 2nd statement so it made some sense to me.
:
A fraction is such that if 5 is added to the numerator and 9 to the denominator, the value of the fraction becomes one third of the numerator.
%28%28n%2B5%29%29%2F%28%28d%2B9%29%29 = 1%2F3n
multiply by 3(d+9), cancel the denominators and you have
3(n + 5) = n(d+9)
3n + 15 = n(d + 9)
:
If the original numerator is doubled and the denominator is increased by 9 the resulting fraction is half the original fraction
(doubling the denominator cuts the fraction in half
n%2F%28%28d%2B9%29%29 =n%2F%282d%29
cross multiply
2dn = n(d+9)
2dn = dn + 9n
2dn - dn = 9n
dn = 9n
divide by n\
d = 9 is the original denominator
d = 9
:
Find n using the 1st equation, replace d with 9
%28%28n%2B5%29%29%2F%28%289%2B9%29%29 = 1%2F3n
%28%28n%2B5%29%29%2F18 = 1%2F3n
multiply equation by 18
n + 5 = 6n
5 = 6n - n
5 = 5n
n = 1 is the original numerator
:
find the number: 1%2F9

Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!
A fraction is such that if 5 is added to the numerator and 9 to the denominator, the value of the fraction becomes one third of the numerator of the original is doubled and the denominator is increased by 9 the resulting fraction is half.find the number 
It would be really nice if you people would proof-read your math problems before submitting them. 



Instead of:

A fraction is such that if 5 is added to the numerator and 9 to the denominator, the value of the fraction becomes

one third of the numerator of the original is doubled and the denominator is increased by 9 the resulting fraction is half. find the number 



It should have been: 

A fraction is such that if 5 is added to the numerator and 9 to the denominator, the value of the fraction becomes

one third. of. If the numerator of the original is doubled and the denominator is increased by 9 the resulting fraction is half. find the number 



Do you see the difference now? I hope you do!

Having said that, the original fraction is: highlight_green%2815%2F51%29