Chapter 7.2, Problem 30WE

To determine

To find: The solution of the proportion.

Answer to Problem 30WE

  $r=x-y$

Explanation of Solution

Given information:

  $\frac{x+y}{y}=\frac{r}{s}$ and $\frac{x-y}{x+y}=\frac{s}{y}$

Calculation:

Given expression,

  $\frac{x+y}{y}=\frac{r}{s}$ and $\frac{x-y}{x+y}=\frac{s}{y}$

Solving the first equation,

  $\Rightarrow \frac{x+y}{y}=\frac{r}{s}$

  $\Rightarrow yr=s(x+y)$

  $\Rightarrow yr=sx+sy\to \text{(i)}$

Solving the second equation,

  $\Rightarrow \frac{x-y}{x+y}=\frac{s}{y}$

  $\Rightarrow s(x+y)=y(x-y)$

  $\Rightarrow sx+sy=yx-y^2$

  $\Rightarrow sx+sy=yx-y^2\to \text{(ii)}$

From equation (i) and (ii),

  $\Rightarrow yr=yx-y^2$

Eliminating y from the whole equation,

  $\Rightarrow r=x-y$

Conclusion:

Therefore, the solution of the proportion is

  $r=x-y$ .