SOLUTION: The numerator and denominator of a fraction are together equal to 100. Increase the numerator by 18 and decrease the denominator by 16 and the fraction is doubled. What is the frac

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: The numerator and denominator of a fraction are together equal to 100. Increase the numerator by 18 and decrease the denominator by 16 and the fraction is doubled. What is the frac      Log On


   

Question 511287: The numerator and denominator of a fraction are together equal to 100. Increase the numerator by 18 and decrease the denominator by 16 and the fraction is doubled. What is the fraction?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The numerator and denominator of a fraction are together equal to 100.
n + d = 100
d = (100-a)
:
Increase the numerator by 18 and decrease the denominator by 16 and the fraction is doubled.
%28%28n%2B18%29%29%2F%28%28d-16%29%29 = %282n%29%2Fd
Cross multiply
d(n+18) = 2n(d-16)
dn + 18d = 2dn - 32n
18d = 2dn - dn - 32n
18d = dn - 32n
:
replace d with (100-n)
18(100-n) = n(100-n) - 32n
1800 - 18n = 100n - n^2 - 32n
:
Arrange as a quadratic equation on the left
n^2 - 18n -100n + 32n + 1800 = 0
n^2 - 86n + 1800 = 0
:
You can use the quadratic formula here but it will factor to:
(n-50){n-36) = 0
Two solutions (remember n + d = 100)
n = 50, then d = 50, but of course 50/50 = 1, not really considered a fraction
and
n = 36, then d = 64
:
36%2F64 is the fraction we want, reduces to 9%2F16
:
:
Check this in the original equation:
%28%2836%2B18%29%29%2F%28%2854-16%29%29 = 54%2F48 reduces to: 18%2F16 twice the original fraction