The numerator of a fraction is 4 less than the denominator. If 17 is added to each, the value of the fraction is 5/6. Find the original fraction
original fraction ----- (x-4)/x
new fraction: (x-14 + 17)/(x + 17) = 5/6
solve for x, then form your fraction
To solve this problem, let's start by setting up the equation based on the given information.
Let's assume that the numerator of the fraction is represented by "x" and the denominator is represented by "x + 4" because the numerator is 4 less than the denominator.
So, the original fraction is x / (x + 4).
According to the problem, if we add 17 to both the numerator and the denominator, the value of the fraction becomes 5/6. So, the new fraction would be (x + 17) / (x + 4 + 17) = 5/6.
Simplifying this equation, we can cross-multiply to get 6(x + 17) = 5(x + 21).
Now, let's solve this equation step by step:
6x + 102 = 5x + 105 (distributed 6 and 5)
Next, we will isolate the variable on one side and simplify:
6x - 5x = 105 - 102
x = 3
Therefore, the numerator (x) of the original fraction is 3, and the denominator (x + 4) is 3 + 4 = 7.
So, the original fraction is 3/7.