SOLUTION: 1: twice the numerator of a fraction exceeds the denominator by 2. if 1 is added to both the numerator and the denominator, the resulting fraction is equal to 2/3. find the orginal

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: 1: twice the numerator of a fraction exceeds the denominator by 2. if 1 is added to both the numerator and the denominator, the resulting fraction is equal to 2/3. find the orginal      Log On


   

Question 586667: 1: twice the numerator of a fraction exceeds the denominator by 2. if 1 is added to both the numerator and the denominator, the resulting fraction is equal to 2/3. find the orginal fraction
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
1: twice the numerator of a fraction exceeds the denominator by 2.
if 1 is added to both the numerator and the denominator, the resulting fraction is equal to 2/3.
find the original fraction.
:
Write an equation for each statement
:
"twice the numerator of a fraction exceeds the denominator by 2"
2n = d + 2
or
d = (2n-2)
:
"if 1 is added to both the numerator and the denominator, the resulting fraction is equal to 2/3"
%28n%2B1%29%2F%28d%2B1%29 = 2%2F3
Cross multiply
2(d+1) = 3(n+1)
2d + 2 = 3n + 3
2d = 3n + 3 - 2
2d = 3n + 1
Replace d with (2n-2)
2(2n-2) = 3n + 1
4n - 4 = 3n + 1
4n - 3n = 1 + 4
n = 5 is the numerator
and
d = 2(5) - 2
d = 8 is the denominator
:
5%2F8 is the original fraction
:
:
Check this; add 1 to the the numerator and the denominator
6%2F9 reduces to 2%2F3