Chapter 9, Problem 12MPS

To determine

To Find: The original fraction.

Answer to Problem 12MPS

  $\frac{9}{12}$

Explanation of Solution

Given: The value of fraction is $\frac{3}{4}$ when $7$ is added to its numerator the resulting fraction is equal to the reciprocal of the original fraction.

Let the fraction be $\frac{x}{y}$

Then

  $\begin{array}{l}\frac{x}{y}=\frac{3}{4}\\ x=3k\\ y=4k\end{array}$

i.e.

The fraction is

  $\frac{3k}{4k}$

When $7$ is added to its numerator

  $\frac{3k+7}{4k}=\frac{4k}{3k}$

Solving for $k$

We get

  $\begin{array}{l}\frac{3k+7}{4k}=\frac{4k}{3k}\\ k=0,3\\ neglecting0\\ k=3\end{array}$

Then

  $\begin{array}{l}x=3k=3\times 3=9\\ y=4k=4\times 3=12\end{array}$

Thus

The fraction becomes

  $\frac{9}{12}$

When $7$ is added to its numerator

  $\frac{9+7}{12}=\frac{16}{12}$

Which is the reciprocal fraction

Hence, the original fraction is $\frac{9}{12}$