SOLUTION: There is a fraction such that if 5 is subtracted from the numerator, its value will be 1/4, and if 7 is added to the denominator, its value will be 1/3. What is the fraction?

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Question 911374: There is a fraction such that if 5 is subtracted from the numerator, its value will be 1/4, and if 7 is added to the denominator, its value will be 1/3. What is the fraction?

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
There is a fraction such that if 5 is subtracted from the numerator, its value will be 1/4,
and if 7 is added to the denominator, its value will be 1/3.
What is the fraction?
:
let n = the numerator
let d = the denominator
:
"if 5 is subtracted from the numerator, its value will be 1/4,"
%28%28n-5%29%29%2Fd = 1%2F4
cross multiply
d = 4(n-5)
d = 4n - 20
"if 7 is added to the denominator, its value will be 1/3."
n%2F%28%28d%2B7%29%29 = 1%2F3
cross multiply
3n = (d+7)
replace d with *(4n-20) (from the 1st statement)
3n = 4n - 20 + 7
3n - 4n = -13
-n = -13
n = 13
Find d
d = 4(13) - 20
d = 52 - 20
d = 32
:
The original fraction = 13%2F32
:
:
You can confirm this, by replacing n and d in both statements