the numerator and denominator of a fraction
are in the ratio 3:2 if 3 is added to the numerator and 2 is subtracted from the denominator a new fraction is formed whose value is 9/4 find the original fraction?
To find the original fraction, we can create a proportion equation using the given information.
Let's assume the numerator of the original fraction is 3x, and the denominator is 2x (since the ratio is given as 3:2).
According to the given information, if 3 is added to the numerator (3x + 3) and 2 is subtracted from the denominator (2x - 2), a new fraction is formed whose value is 9/4.
We can write this as an equation:
(3x + 3) / (2x - 2) = 9/4
To solve this equation for x, we'll need to cross-multiply:
4(3x + 3) = 9(2x - 2)
Simplifying further:
12x + 12 = 18x - 18
Now, let's isolate the variables on one side of the equation:
12 + 18 = 18x - 12x
30 = 6x
Dividing both sides by 6:
30/6 = x
x = 5
Now that we have the value of x, we can substitute it back into the original assumption:
Numerator = 3x = 3 * 5 = 15
Denominator = 2x = 2 * 5 = 10
Therefore, the original fraction is 15/10, which simplifies to 3/2.
n/d = 3/2
(n+3)/(d-2) = 9/4
n/d = 15/10