When 5 is added to both the numerator and denominator of a fraction the result becomes 1/2.When 1 is subtracted from both the numerator and denominator the fraction becomes 1/5.Find the fraction. plzz do whole method, i cant understand it.

original fraction: x/y

case1 (x+5)/(y+5) = 1/2
2x + 10 = y+5
2x - y = -5 **

case2 (x-1)/(y-1) = 1/5
5x - 5 = y - 1
5x - y = 4 ***

subtract ** from ***
3x = 9
x = 3, then from ** 6 - y = -5 , y = 11

the original fraction was 3/11

check: (3+5)/(11+5) = 8/16 = 1/2, check!
(3-1)/(11-1) = 2/10 = 1/5, check!

My answer is correct

To solve this problem, let's first assign variables to represent the numerator and denominator of the fraction. Let's say the numerator is represented by the variable 'x' and the denominator is represented by the variable 'y'.

According to the problem statement, when 5 is added to both the numerator and denominator, the fraction becomes 1/2. This can be written as:

(x + 5)/(y + 5) = 1/2

Next, when 1 is subtracted from both the numerator and denominator, the fraction becomes 1/5. This can be written as:

(x - 1)/(y - 1) = 1/5

We now have a system of two equations with two variables. We can solve this system using the method of substitution or elimination. Let's use the method of substitution.

From the first equation, we can express 'x' in terms of 'y' by cross-multiplying:

2(x + 5) = y + 5

Simplifying this equation gives:

2x + 10 = y + 5

Rearranging this equation yields:

y = 2x + 5 - 10
y = 2x - 5 ---(Equation 1)

Now, let's substitute this expression for 'y' into the second equation:

(x - 1)/(2x - 6) = 1/5

Cross-multiplying and simplifying this equation gives:

5(x - 1) = (2x - 6)

Expanding and rearranging, we get:

5x - 5 = 2x - 6
5x - 2x = -6 + 5
3x = -1
x = -1/3

Now that we have found the value of 'x', we can substitute this back into Equation 1 to find the value of 'y':

y = 2x - 5
y = 2(-1/3) - 5
y = -2/3 - 15/3
y = -17/3

Therefore, the fraction is (-1/3) / (-17/3), which can be simplified by multiplying both the numerator and denominator by -3:

((-1/3) * (-3)) / ((-17/3) * (-3))
1 / 17

So, the fraction is 1/17.