A fraction becomes when 1 is added to each numerator and denominator. However, if we subtracted 5 from each, then it becomes . The fraction is :
Question
A fraction becomes when 1 is added to each numerator and denominator. However, if we subtracted 5 from each, then it becomes . The fraction is :
Solution
The problem is asking to find a fraction which satisfies two conditions:
- When 1 is added to both the numerator and the denominator, the fraction becomes 1/2.
- When 5 is subtracted from both the numerator and the denominator, the fraction becomes 1/3.
Let's denote the numerator as x and the denominator as y.
From the first condition, we can write the equation as (x+1)/(y+1) = 1/2.
From the second condition, we can write the equation as (x-5)/(y-5) = 1/3.
Now we have a system of two equations:
- 2x + 2 = y + 1
- 3x - 15 = y - 5
Solving these equations simultaneously, we find that x = 7 and y = 8.
Therefore, the fraction is 7/8.
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