Question

If the numerator of a fraction is increased by 3, the fraction becomes 3/4.If the denominator is decreased by 7,the fraction becomes 1. Determine the original fraction.

Answer 1

9/16

Explanation:

Let the original fraction be

x/y

Then

x+3/y=3/4

and

x/y-7=1

Look at 2nd fraction, rearrange it such that you multiply by "y-7" on both sides

x=y-7

Substitute this into 1st fraction:

x-7+3/y=3/4

Now we can solve this for y: cross-multiply --> (Note: y-7+3 = y-4)

4(y-4)=3y

y=16

Sub this back into "x = y-7" to get x

x=16-7=9

Therefore the original fraction is:

9/16