Question

The denominator of a fraction is four more than three times the numerator. if both numerator and denominator are increased by four, the simplified result is 925925. find the original fraction. (do not simplify.)

Answer 1

Let's call the numerator $x$. Since the denominator is four more than three times the numerator, it means that it equals $3x+4$. So, the original fraction is

$\frac{x}{3x+4}$

Note that this implies that $x \neq \frac{-4}{3}$, otherwise the denominator would be zero. Now, we need to increase both numerator and denominator by 4, obtaining this new fraction:

$\frac{x+4}{3x+4+4} = \frac{x+4}{3x+8}$

Note that this implies that $x \neq \frac{-8}{3}$, otherwise the denominator would be zero. And we know that this equals 925 (assuming that 925925 is some kind of typo/formatting error). This leads to the equation

$\frac{x+4}{3x+8} = 925$

Since we assumed that the denominator is not zero, we can multiply both sides by it, so that the equation becomes

$x+4 = 925(3x+8) = 7400 + 2775 x$

Subtract 4 from both sides to get

$x = 7396 + 2775 x$

Subtract 2775x from both sides to get

$-2774 x = 7396$

Finally, divide both sides by -2774 to get

$x = \frac{7396}{-2774}$