SOLUTION: 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.
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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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