Chapter 7.3, Problem 41HP

To determine

To explain:the given statement

Answer to Problem 41HP

Here, $\text{x\% of y}$ and $y\%\text{ of }x$ is equivalent.

Explanation of Solution

Given:

Is $x\%$ of y and $y\%$ of x always, sometimes, or never equivalent

Calculation:

Let n be the number.

  $\begin{array}{l}x\%\text{ of }y:\\ \frac{x}{100}=\frac{n}{y}\\ x\times y=n\times 100\\ \frac{xy}{100}=n\end{array}$

  $\begin{array}{l}y\%\text{ of }x:\\ \frac{y}{100}=\frac{n}{x}\\ x\times y=n\times 100\\ \frac{xy}{100}=n\end{array}$

Conclusion:

Therefore, $x\%\text{ of y}$ and $y\%\text{ of }x$ is equivalent.