The denominator of a fraction is 20 more than the numerator of the fraction. If 5 is added to the numerator of the fraction and the denominator is unchanged, the value of the resulting fraction becomes 38. Use x as your variable. Find x.
Even with 5 added, with the denominator being 20 more, the result cannot be a whole number. Typos?
(x + 5) / (x + 20) = 38
x + 5 = 38x + 760
-37x = 755
To solve this problem, let's start by assigning variables to the numerator and denominator of the fraction. We'll let x represent the numerator.
According to the problem, the denominator is 20 more than the numerator. So we can express the denominator as x + 20.
Now, let's set up an equation based on the information that if 5 is added to the numerator and the denominator is unchanged, the resulting fraction becomes 38. We can write this as:
(x + 5) / (x + 20) = 38
To solve this equation, we can start by cross-multiplying:
(x + 5) * 1 = 38 * (x + 20)
Simplifying further:
x + 5 = 38x + 760
Next, let's isolate the x term by subtracting x from both sides of the equation:
5 = 37x + 760
Subtracting 760 from both sides:
-755 = 37x
Finally, divide both sides of the equation by 37 to solve for x:
x = -755 / 37
Using a calculator, we find that x is approximately -20.41.
So, the value of x is approximately -20.41.