this needs to be solved by substitution

Question

if 1 is subtracted from the numerator of a fraction, the value of the resulting fraction is one half. However, if seven is added to the denominator of the original fraction, the value of the resulting fraction is one third. Find the original fraction 

Answer 1

(x - 1) / y = 1/2

x / (y + 7) = 1/3

To solve this, we need to isolate a variable. Let's make it the y-variable:

First equation:

x - 1 = y/2

2x - 2 = y

Second equation:

x = (y + 7) / 3

3x = y + 7

3x - 7 = y

Now that we have both equations equaling y, that means they equal one another

2x - 2 = 3x - 7

-2 = x - 7

5 = x

 

5 * 2 - 2 = y

10 - 2 = y

8 = y

Check our answer: 

5 * 3 - 7 = y

15 - 7 = y

8 = y

 

Let's test:

(5 - 1) / 8 = 1/2

4/8 = 1/2

1/2 = 1/2

 

5/(8 + 7) = 1/3

5/15 = 1/3

1/3 = 1/3