Question 738312: 12. The sum of numerator and denominator of a fraction is 8. I 3 is added to both numerator and denominator, the fraction becomes ¾. Find the fraction.
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! THE FIFTH-GRADER WAY:
after adding 3 to numerator and denominator the new fraction is
 = .....
If the new fraction was  , the original fraction would have been  . That is just zero, which is not much of a fraction, and even if you say that the numerator is  and the denominator is  , the sum of numerator plus denominator would be  , which is not  .
If the new fraction was  , the original fraction would have been  , and that is a solution to the problem, because  .
since the wording suggests that there is one solution, no need to try  ,  , etc, but it is clear that those would make an original fraction with a sum of numerator plus denominator greater than .
THE ALGEBRA WAY:
 = the fraction
 = the numerator
 = the denominator
The sum of numerator and denominator of a fraction is 8 translates into
If 3 is added to both numerator and denominator, the fraction becomes translates into
 -->  -->  --> 
Now we have to solve the system 
We solve it any way we can to find  and 
SUBSTITUTION:
-->
 -->  -->
 -->  -->  -->  --> -->
Then  -->  -->
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