The numerator of a fraction is 4 less than twice the denominator. If both the numerator and the denominator are increased by 1, the fraction becomes 3/2. What is the original fraction?
n = 2d-4
(n+1)/(d+1) = 3/2
(2d-4+1)/(d+1) = 3/2
2(2d-3) = 3(d+1)
4d-6 = 3d+3
d = 9
So, the original fraction is 14/9
To solve this problem, we need to set up an equation based on the given information.
Let's assume that the denominator of the original fraction is "x".
According to the problem, the numerator of the original fraction is 4 less than twice the denominator, which can be written as 2x - 4.
Therefore, the original fraction can be written as (2x - 4)/x.
Now, we are told that if both the numerator and the denominator are increased by 1, the fraction becomes 3/2.
Therefore, the new fraction can be written as (2x - 4 + 1)/(x + 1), which simplifies to (2x - 3)/(x + 1).
We can set up the equation: (2x - 3)/(x + 1) = 3/2.
To solve this equation, we can cross-multiply:
2 * (2x - 3) = 3 * (x + 1)
4x - 6 = 3x + 3
Now, we can solve for x:
4x - 3x = 3 + 6
x = 9
So the denominator of the original fraction is 9.
To find the numerator of the original fraction, we substitute the value of x back into the expression for the numerator: 2x - 4.
Numerator = 2(9) - 4 = 18 - 4 = 14.
Therefore, the original fraction is 14/9.