The numerator of a certain fraction is 3 times the denominator. If the numerator is decreased by 1 and the denomenator is increased by 2, the value of the resulting fraction is 5/2. Find the fraction.
N=3D and
(N-1)/(D+2)=5/2
or 2N-2=5D+10 or
2N=5D+12
solve.
3 hahaha!
The numerator of a certain fraction is 4 times the denominator. If 12 is added to both the numerator and the denominator, the resulting fraction is equivalent to 2. What was the original fraction.
To solve this problem, we can set up two equations based on the given information.
Let's call the numerator of the fraction N and the denominator D.
1) We are given that the numerator (N) is 3 times the denominator (D), so we can write this as:
N = 3D
2) We are also given that if we decrease the numerator by 1 and increase the denominator by 2, the resulting fraction is 5/2. We can express this as the following equation:
(N - 1) / (D + 2) = 5/2
Now we can use these two equations to find the values of N and D.
First, let's substitute the value of N from equation (1) into equation (2):
(3D - 1) / (D + 2) = 5/2
Next, let's cross-multiply to eliminate the fractions:
2(3D - 1) = 5(D + 2)
Expand the equation:
6D - 2 = 5D + 10
Move the variables to one side and the constants to the other side:
6D - 5D = 10 + 2
D = 12
Now substitute the value of D back into equation (1) to find N:
N = 3D
N = 3 * 12
N = 36
So the fraction is 36/12, which can be simplified to 3/1 or simply 3.
Therefore, the fraction is 3/1.