SOLUTION: in a certain fraction, the denominator is 4 less than twice the numerator. If 15 is added to the numerator and subtracted from the denominator, the value of the fraction is 4. Find

Algebra ->  Rate-of-work-word-problems -> SOLUTION: in a certain fraction, the denominator is 4 less than twice the numerator. If 15 is added to the numerator and subtracted from the denominator, the value of the fraction is 4. Find      Log On


   

Question 468376: in a certain fraction, the denominator is 4 less than twice the numerator. If 15 is added to the numerator and subtracted from the denominator, the value of the fraction is 4. Find the original fraction.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
in a certain fraction, the denominator is 4 less than twice the numerator.
If 15 is added to the numerator and subtracted from the denominator, the value of the fraction is 4.
Find the original fraction.
:
Write an equation for each statement
:
"the denominator is 4 less than twice the numerator."
d = 2n - 4
:
"If 15 is added to the numerator and subtracted from the denominator, the value of the fraction is 4."
%28n%2B15%29%2F%28d-15%29 = 4
n + 15 = 4(d-15)
n + 15 = 4d - 60
n = 4d - 60 - 15
n = 4d - 75
replace d with (2n-4)
n = 4(2n-4) - 75
n = 8n - 16 - 75
n - 8n - 91
91 = 8n - n
91 = 7n
n = 91%2F7
n = 13 is the numerator
then
d = 2(13) - 4
d = 22
:
13%2F22 is the original fraction
:
:
Check this in the statement
"If 15 is added to the numerator and subtracted from the denominator, the value of the fraction is 4."
%2813%2B15%29%2F%2822-15%29 = 28%2F7 = 4