this needs to be solved using substitution

Question

 is the numerator of a fraction is increased by four, the value of the resulting fraction is three fourths. If the denominator of the original fraction is increased by two, the value of the resulting fraction is one half. Find the original fraction 

Answer 1

(x + 4) / y = 3/4

x / (y + 2) = 1/2

 

Just like before, we need to isolate a variable.

First equation, start by multiplying both sides by y:

x + 4 = 3y/4

Now multiply both sides by 4/3:

4(x + 4) / 3 = y

 

Second equation, start by multiplying both sides by y + 2:

x = (y + 2) / 2

2x = y + 2

2x - 2 = y

 

Again, both equations equal y, so they equal one another:

4(x + 4) / 3 = 2x - 2

4(x + 4) = 3(2x - 2)

4x + 16 = 6x - 6

16 = 2x - 6

22 = 2x

11 = x

 

Now to find and check y:

4(11 + 4) / 3 = y

60 / 3 = y

20 = y

 

2 * 11 - 2 = y

22 - 2 = y

20 = y

 

Now to test.

(11 + 4) / 20 = 3/4

15 / 20 = 3/4

3/4 = 3/4

 

11 / (20 + 2) = 1/2

11/22 = 1/2

1/2 = 1/2