SOLUTION: A numerator is 3 less than the denominator. If each is increased by one, the new fraction is 10/11. What is the original fraction?

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: A numerator is 3 less than the denominator. If each is increased by one, the new fraction is 10/11. What is the original fraction?      Log On


   

Question 1137536: A numerator is 3 less than the denominator. If each is increased by one, the new fraction is 10/11. What is the original fraction?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
let the original fraction be n%2Fd
:
A numerator is 3 less than the denominator.
n = d-3
If each is increased by one, the new fraction is 10/11.
%28%28n%2B1%29%29%2F%28%28d%2B1%29%29 = 10%2F11
cross multiply
11(n+1) = 10(d+1)
11n + 11 = 10d + 10
11n = 10d + 10 - 11
11n = 10d - 1
replace n with (d-3)
11(d-3) = 10d - 1
11d - 33 = 10d = 1
11d - 10d = -1 + 33
d = 32
find n
n = 32-3
n = 29
The original fraction 29%2F32
:
:
Check, adding 1 to n & d = 30/33 which reduces to 10/11