If nine is added to both the numerator and the denominator of a certain fraction, the fraction becomes 3/4. If one is subtracted from both the numerator and the denominator, it becomes 1/2. The fraction is
Question
If nine is added to both the numerator and the denominator of a certain fraction, the fraction becomes 3/4. If one is subtracted from both the numerator and the denominator, it becomes 1/2. The fraction is
Solution
Let's denote the numerator as x and the denominator as y.
From the problem, we have two equations:
- x + 9 / y + 9 = 3/4
- x - 1 / y - 1 = 1/2
We can solve these two equations simultaneously to find the values of x and y.
First, let's simplify the equations:
- 4x + 36 = 3y + 27
- 2x - 2 = y - 1
Solving these equations, we get:
- 4x - 3y = -9
- 2x - y = 3
Multiplying the second equation by 2, we get:
4x - 2y = 6
Subtracting this from the first equation, we get:
-y = -15
So, y = 15.
Substituting y = 15 into the second equation, we get:
2x - 15 = 3
So, x = 9.
Therefore, the fraction is 9/15.
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