Chapter 9, Problem 9CR

To determine

To Find: The original fraction?

Answer to Problem 9CR

  $\frac{2}{9}$

Explanation of Solution

Given: The denominator of the fraction is $7$ more than the numerator. If $5$ is added to each, the value of the resulting fraction is $\frac{1}{2}$ .

Let $n$ be the numerator

The denominator of the fraction is $7$ more than the numerator

i.e.

Original fraction

  $\frac{n}{n+7}$

Now $5$ is added to each, the value of the resulting fraction is $\frac{1}{2}$ .

We get

  $\frac{n+5}{n+7+5}=\frac{1}{2}$

Solving for $n$

  $\begin{array}{l}\frac{n+5}{n+12}=\frac{1}{2}\\ 2(n+5)=n+12\\ 2n+10=n+12\\ n=2\end{array}$

Substitute $n=2$ in original fraction

  $\begin{array}{l}\frac{n}{n+7}\\ \frac{2}{2+7}=\frac{2}{9}\end{array}$

Hence, original fraction is $\frac{2}{9}$