The denominator of a fraction is 12 more than the numerator. If 16 is added to the numerator and 16 is subtracted from the denominator, the value of the resulting fraction is equal to 2/1. Find the original fraction
"The denominator of a fraction is 12 more than the numerator."
let x = the numerator
x+12 = the denominator
"If 16 is added to the numerator and 16 is subtracted from the denominator, the value of the resulting fraction is equal to 2/1"
(x+16) / (x+12-16) = 2/1
x = ?
Use x to find the original numerator and denominator based on the first statement.
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What is the answer
To find the original fraction, let's start by setting up equations based on the given information.
Let's assume the numerator of the fraction is represented by the variable "x." According to the problem, the denominator is 12 more than the numerator, so it can be represented by "x + 12."
The resulting fraction, when 16 is added to the numerator and subtracted from the denominator, is equal to 2/1. So we can set up the following equation:
(x + 16) / (x + 12 - 16) = 2 / 1
We can simplify this equation further:
(x + 16) / (x - 4) = 2
Next, we can cross-multiply to eliminate the denominator:
2(x - 4) = x + 16
Expanding both sides of the equation:
2x - 8 = x + 16
Moving all terms with "x" to one side and constants to the other side:
2x - x = 16 + 8
x = 24
So the numerator of the original fraction is 24.
Since the denominator is 12 more than the numerator, the denominator is x + 12, which is 24 + 12 = 36.
Therefore, the original fraction is 24/36.