the numerator and denominator of a fraction
are in the ratio 3:2 if three is added to the numerator and three is subtracted from the denominator a new fraction is formed whose value is 9/4 find the original fraction?
n/d = 3/2
(n+3)/(d-3) = 9/4
I don't get two integer values for n and d. Typo?
To solve this problem, we can break it down into several steps:
Step 1: Set up the equation to represent the given information
Let's assume the numerator of the original fraction is 3x and the denominator is 2x, where x is the common ratio between them. The original fraction can be expressed as (3x/2x).
Step 2: Apply the given condition and create a new fraction
According to the problem, if we add 3 to the numerator and subtract 3 from the denominator, we get a new fraction with a value of 9/4. So the new fraction can be expressed as ((3x + 3)/(2x - 3)).
Step 3: Set up the equation using the new fraction
Now we need to set up an equation using the new fraction:
((3x + 3)/(2x - 3)) = 9/4
Step 4: Solve the equation
To solve the equation, we can multiply both sides by 4(2x - 3) to eliminate the denominators:
4(2x - 3) * ((3x + 3)/(2x - 3)) = (9/4) * (4(2x - 3))
After canceling out the common factors, we have:
4(3x + 3) = 9(2x - 3)
Simplifying further:
12x + 12 = 18x - 27
Step 5: Solve for x
To solve for x, we'll move all the terms involving x to one side of the equation and the constant terms to the other side:
12 + 27 = 18x - 12x
39 = 6x
Divide both sides by 6 to find the value of x:
x = 39/6 = 6.5
Step 6: Find the original fraction
Now that we have the value of x, we can substitute it back into the expression for the original fraction:
Original numerator = 3x = 3 * 6.5 = 19.5
Original denominator = 2x = 2 * 6.5 = 13
Therefore, the original fraction is 19.5/13.