Chapter 6, Problem 4CR

To determine

The solution of the percent problem “ $8$ hours is what percent of $24$ hours?” with equation.

Answer to Problem 4CR

  $33.3\%$

Explanation of Solution

Given:

The percent problem “ $8$ hoursis what percent of $24$ hours?”.

Concept used:

To translate a phrase of the form “ $A$ is what percent of $B$ ?” to an equation. First, assume that the percent is x . Then, read the statement “ $A$ is $x\%$ of $B$ ”. In “ $x\%$ of $B$ ” the word “of” represents “multiplication”. So, the given statement can be translated in to an equation as follows:

  $\begin{array}{ccccc}\text{A}& \text{is}& \text{what percent}& \text{of}& B\\ \downarrow & \downarrow & \downarrow & \downarrow & \downarrow \\ A& =& x& ·& B\end{array}$

So, the equation becomes $A=x·B$ .

Calculation:

Using the concept, the given statement can be translated into an equation as

  $8=x\cdot 24$ .

Now, solve the equation as follows:

  $\begin{array}{c}\text{ 8}=x\cdot 24\\ \frac{8}{24}=\frac{x\cdot 24}{24}\text{Divide both sides with 24}\text{.}\\ \frac{8}{24}=x\\ 0.333=x\\ x=0.333\end{array}$

Next, since we are looking for percent, we can write $0.333$ as a percent.

  $x=33.3\%$

Conclusion:

The solution of the percent problem is $33.3\%$ .