SOLUTION: when a fraction is reduced to its lowest term, it is equal to 3/4. The numerator of the fraction when doubled would be 34 greater than the denominator. Find the fraction.

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: when a fraction is reduced to its lowest term, it is equal to 3/4. The numerator of the fraction when doubled would be 34 greater than the denominator. Find the fraction.      Log On


   

Question 891932: when a fraction is reduced to its lowest term, it is equal to 3/4. The numerator of the fraction when doubled would be 34 greater than the denominator. Find the fraction.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The first part gives the fraction. The second part gives a description between numerator and denominator.

n for numerator;
d for denominator.

n%2Fd=3%2F4. This shows ratio between n and d, regardless of reduced or in other terms.

2n=34%2Bd, notice from the wording, "would be 34 greater", meaning ADDITION.
That could be a reason why you found the question difficult.

d=2n-34;
substitute into the reduced-form equation.
highlight_green%28n%2Fd=highlight_green%28n%2F%282n-34%29=3%2F4%29%29.
Solve the inner-green outlined part for n.
-
4n=3%282n-34%29
4n=6n-3%2A34
4n-6n=-3%2A34
-2n=-3%2A34
2n=3%2A34
n=3%2A17
highlight%28n=51%29
-
d=2%2A51-34
d=102-34
highlight%28d=68%29

CHECK:
n%2Fd=highlight%2851%2F68%29=%283%2A17%29%2F%284%2A17%29=3%2F4
YES.

(Notice in the "CHECK", the n%2Fd is outlined in red.)


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I made the same mistake that you probably made, when going through the problem the first time.