Question

The denominator of a fraction is five more than the numerator. If both the numerator and denominator are decreased by 3, the simplified result is 7/8. Find the original fraction. Do NOT simplify.

Answer 1

We are going to formulate the equation mentioned in the statement

$\frac{x-3}{x+5-3}=\frac{7}{8}$

Now let's solve the problem

$\begin{gathered} \frac{x-3}{x+5-3}=\frac{7}{8} \\ \frac{x-3}{x+2}=\frac{7}{8} \\ 8\left(x-3\right)=7\left(x+2\right) \\ 8x-24=7x+14 \\ 8x-7x=24+14 \\ x=38 \\ \end{gathered}$

Now we calculate the values for the original equation

$\begin{gathered} \frac{38}{38+5} \\ \frac{38}{43} \end{gathered}$

The solution would be 38/43