The value of the numerator of a particular fraction is one-half the value of its denominator. If the numerator is increased by 2 and the denominator is decreased by 2, the value of the resulting fraction is 3/4. What is the denominator of the original fraction?
Let the numberator = x
Then the denominator = 2x
So...we have this
x + 2 3
_______ = ____ cross-multiply
2x - 2 4
4 ( x + 2) = 3 (2x - 2) simplify
4x + 8 = 6x - 6 add 6 to both sides, subtract 4x from both sides
2x = 14 divide both sides by 2
x = 7
The denominator of the original fraction = 2x = 2(7) = 14