SOLUTION: If both the numerator and the denominator of a certain fraction are increased by 1, it becomes 5/6.if both the numerator and denominator are each decreased by 1 it becomes 4/5.find

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Question 665756: If both the numerator and the denominator of a certain fraction are increased by 1, it becomes 5/6.if both the numerator and denominator are each decreased by 1 it becomes 4/5.find the original fraction
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
If both the numerator and the denominator of a certain fraction are increased by
1, it becomes 5/6.if both the numerator and denominator are each decreased by 1
it becomes 4/5.find the original fraction
:
"If both the numerator and the denominator of a certain fraction are increased by 1, it becomes 5/6."
%28%28n%2B1%29%29%2F%28%28d%2B1%29%29 = 5%2F6
Cross multiply
6(n+1) = 5(d+1)
6n + 6 = 5d + 5
6n - 5d = 5 - 6
6n - 5d = -1
:
" both the numerator and denominator are each decreased by 1 it becomes 4/5."
%28%28n-1%29%29%2F%28%28d-1%29%29 = 4%2F5
Cross multiply
5(n-1) = 4(d-1)
5n - 5 = 4d - 4
5n - 4d = -4 + 5
5n - 4d = 1
:
We can use elimination here, Mult the 1st eq by 4, mult the 2nd eq by 5
Subtract the 1st equation from the 2nd equation
25n - 20d = 5
24n - 20d = -4
--------------- Subtraction eliminates d, find n
n = 9
:
find d using 5n - 4d = 1
5(9) - 4d = 1
45 - 4d = 1
-4d = 1 - 45
-4d = 44
d = +11
:
9%2F11 is the original equation, you check this for yourself