SOLUTION: The denominator of the fraction is 2 more than the numerator. If 1 is subtracted from the numerator and 2 is added to the denominator the numerator becomes half of the denominat

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Question 1148005: The denominator of the fraction is 2 more than the numerator. If 1 is subtracted
from the numerator and 2 is added to the denominator the numerator becomes half
of the denominator find the fraction.
Found 3 solutions by josgarithmetic, Edwin McCravy, ikleyn:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
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The denominator of the fraction is 2 more thn the numerator
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If 1 is subtracted from numerator and 2 is added to denominator
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the numerator becomes half of the denominator
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------------solve this...
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
The denominator of the fraction is 2 more than the numerator
 

D = N + 2

If 1 is subtracted from the numerator 
NEW numerator = N-1

and 2 is added to the denominator 
NEW denominator = D+2

the (NEW) numerator becomes half of the (NEW) denominator.
NEW numerator = N-1 = (1/2)(D+2) 

Multiply both sides by 2:

             2(N-1) = 2(1/2)(D+2)
               2N-2 = D+2
               2N-D = 4

So we have the system of two equations in two unknowns:



YOU solve that system for the values of N and D by substitution.

find the fraction.
Put the original numerator, the value of N, over D, the
value of the denominator.  DO NOT REDUCE THE FRACTION!!!

Edwin
Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.

Let n = the numerator;  then the denominator = (n+2).


The condition says


    n-1 = 


Multiply both sides by 2 and then simplify


    2n - 2 = ((n+2) + 2

    2n - 2 = n + 4

    2n - n = 4 + 2

     n     = 6


ANSWER.  The numerator is 6;  the denominator is 6+2 = 8.

         The fraction is   = .    ANSWER

SOLVED.


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