SOLUTION: if the numerator of a certain fraction is increased by 6 and its denominator is decreased by 5, the resulting fraction is equal to 3/4. if the reciprocal of the original fraction i

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Question 151027: if the numerator of a certain fraction is increased by 6 and its denominator is decreased by 5, the resulting fraction is equal to 3/4. if the reciprocal of the original fraction is decreased by 1, the resulting fraction is 16/9. find the original fraction.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
if the numerator of a certain fraction is increased by 6 and its denominator is decreased by 5, the resulting fraction is equal to 3/4. if the reciprocal of the original fraction is decreased by 1, the resulting fraction is 16/9. find the original fraction.
:
Let "a certain fraction" = n%2Fd
and
"if the numerator of a certain fraction is increased by 6 and its denominator is decreased by 5, the resulting fraction is equal to 3/4."
%28%28n%2B6%29%29%2F%28%28d-5%29%29 = 3%2F4
and
"If the reciprocal of the original fraction is decreased by 1, the resulting fraction is 16/9."
d%2Fn - 1 = 16%2F9
Add 1 to both sides:
d%2Fn = 16%2F9 + 9%2F9
d%2Fn = 25%2F9
That means:
n = 9
-- --- is the original fraction
d = 25
:
Using the 1st statment to check this:
%28%289%2B6%29%29%2F%28%2825-5%29%29 = 15%2F20 = 3%2F4