Chapter 7, Problem 8CPE

To determine

To find: $\frac{r+s}{t+u}=\frac{?}{?}$

Answer to Problem 8CPE

  $\frac{r+s}{t+u}=\frac{s}{u}$

Explanation of Solution

Given information:

  $\frac{r}{s}=\frac{t}{u}$

Calculation:

Properties of proportion states that,

$\frac{a}{b}=\frac{c}{d}$ is equivalent to $\frac{a+b}{b}=\frac{c+d}{d}$

Then,

  $\begin{array}{l}\frac{r}{s}=\frac{t}{u}\\ \Rightarrow \frac{r+s}{s}=\frac{t+u}{u}\\ \Rightarrow \frac{r+s}{t+u}=\frac{s}{u}[\because \frac{a}{b}=\frac{c}{d}\text{is equivalent to }\frac{a}{c}=\frac{b}{d}]\end{array}$

Thus, if $\frac{r}{s}=\frac{t}{u}$, then, $\frac{r+s}{t+u}=\frac{s}{u}$ .