Chapter 7, Problem 8CR

To determine

Find whether the given equation is equivalent to the proportion $\frac{30-x}{x}=\frac{8}{7}$ .

Answer to Problem 8CR

Yes.

Explanation of Solution

Given:

The equation is :

  $\frac{30}{x}=\frac{15}{7}$

Calculation:

Solve $\frac{30-x}{x}=\frac{8}{7}$

  $\begin{array}{l}\frac{30-x}{x}=\frac{8}{7}\\ \Rightarrow 7(30-x)=8x\mathrm{...............}[\text{multiply each side by 7x]}\\ \Rightarrow 210-7x=8x\\ \Rightarrow 210=15x\mathrm{......................}[\text{add 7x each side]}\\ \Rightarrow x=\frac{210}{15}\mathrm{........................}[\text{divide each side by 15]}\\ \Rightarrow x=14\end{array}$

Given equation is

  $\begin{array}{l}\frac{30}{x}=\frac{15}{7}\\ \Rightarrow 210=15x\mathrm{.............}[\text{multiply each side by 7x]}\\ \Rightarrow x=\frac{210}{15}\mathrm{................}[\text{divide each side by 15]}\\ \Rightarrow x=14\end{array}$

Since the solution of both the equations is same, so the are equivalent.