Final answer:
To solve the problem, assume the original fraction is x/y. Use the given information to set up an equation and solve for y. Substitute the value of y back into the equation x = y - 3 to find x. The original fraction is x/y.
Step-by-step explanation:
To solve this problem, let's assume the original fraction is x/y, where x is the numerator and y is the denominator.
According to the given information, x = y - 3.
When both the numerator and denominator are increased by 4, the new fraction is (x + 4) / (y + 4). We also know that this new fraction is increased by 4/15.
Setting up the equation, we have: (x + 4) / (y + 4) = x/y + 4/15.
Substituting the value of x from the first equation, we have: (y - 3 + 4) / (y + 4) = (y - 3)/y + 4/15.
Simplifying this equation, we get: (y + 1) / (y + 4) = (15y - 45 + 4y) / (15y).
By cross-multiplication, we can solve for y.
After finding the value of y, substitute it back into the equation x = y - 3 to get the value of x.
The original fraction is x/y.