The denominator of a fraction is 4 more than the numerator. If both the numerator and the denominator are increased by 1, the fraction becomes 4/5. What is the original fraction?
To find the original fraction, let's start by assigning variables to the numerator and the denominator.
Let's say the numerator is "x".
According to the given information, the denominator is 4 more than the numerator, so we can write it as "x + 4".
The original fraction can be represented as "x / (x + 4)".
Now, let's consider the second part of the problem, where both the numerator and the denominator are increased by 1. The new fraction is 4/5, which can be written as "4 / (5)".
Since the second fraction is the result of increasing both the numerator and the denominator of the original fraction by 1, we can set up the equation:
(x+1) / (x+4+1) = 4 / 5
Simplifying the equation, we have:
(x+1) / (x+5) = 4 / 5
Cross-multiplying, we get:
5(x+1) = 4(x+5)
Expanding both sides of the equation, we have:
5x + 5 = 4x + 20
Subtracting 4x from both sides, we get:
x + 5 = 20
Subtracting 5 from both sides, we get:
x = 15
So, the numerator of the original fraction is 15, and the denominator is 4 more, which is 15 + 4 = 19.
Therefore, the original fraction is 15/19.
69 is not a fraction.
d = n+4
(n+1)/(d+1) = 4/5
(n+1)/(n+4+1) = 4/5
(n+1)/(n+5) = 4/5
5(n+1) = 4(n+5)
5n+5 = 4n+20
n = 15
The fraction was 15/19