Chapter 11, Problem 6MPS

To determine

To find: the original fraction.

Answer to Problem 6MPS

The 0riginal fraction is $\frac{57}{95}$ .

Explanation of Solution

Given information:

If numerator and denominator is increased by $3$ . The resulting fraction is $\frac{5}{8}$ .

The fractions value is $\frac{3}{5}$

Calculation:

Assume that the fraction is $\frac{p}{q}$ .

As per given information,

  $\begin{array}{l}\frac{p}{q}=\frac{3}{5}\\ 5p=3q\\ p=\frac{3q}{5}\end{array}$ ..... (1)

If numerator and denominator is increased by $3$ . The resulting fraction is $\frac{5}{8}$ .

  $\begin{array}{l}\frac{p+3}{q+3}=\frac{5}{8}\\ 8p+24=5q+15\\ 8p-5q=-19\end{array}$ ..... (2)

Substitute the value of $p$ in equation (2).

  $\begin{array}{l}8\left(\frac{3q}{5}\right)-5q=-19\\ \frac{24q}{5}-5q=-19\\ \frac{24q-25q}{5}=-19\\ q=95\end{array}$

Substitute the value of $q$ in equation (1).

  $\begin{array}{c}p=\frac{3\left(95\right)}{5}\\ =57\end{array}$

The fraction will be,

  $\frac{p}{q}=\frac{57}{95}$

Therefore, the o0riginal fraction is $\frac{57}{95}$ .