SOLUTION: The numerator of a fraction is 2 less than its denominator. If 3 is subtracted from the numerator and from the denominator, the new fraction obtained is 3/4. Find the fraction.

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: The numerator of a fraction is 2 less than its denominator. If 3 is subtracted from the numerator and from the denominator, the new fraction obtained is 3/4. Find the fraction.      Log On


   

Question 1120905: The numerator of a fraction is 2 less than its denominator. If 3 is subtracted from the numerator and from the denominator, the new fraction obtained is 3/4. Find the fraction.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Using formal algebra....

Let the original fraction be x%2F%28x%2B2%29.

3 subtracted from both numerator and denominator makes the fraction %28x-3%29%2F%28x-1%29.

We want that new fraction to have the value 3/4:

%28x-3%29%2F%28x-1%29+=+3%2F4
3x-3+=+4x-12
x+=+9

The original fraction is x/(x+2) = 9/11.

Using logical reasoning....

When 3 is subtracted from both numerator and denominator, the numerator is still 2 less than the denominator. So look for a fraction equivalent to 3/4 in which the numerator is 2 less than the denominator.

In the fraction 3/4, the numerator is 1 less than the denominator; multiplying numerator and denominator by 2 will give us a fraction equivalent to 3/4 in which the numerator is 2 less than the denominator: 3/4 = 6/8.

So 6/8 is the fraction after 3 has been subtracted from both numerator and denominator; that means the original fraction was 9/11.