Chapter 6, Problem 3CR

To determine

The solution of the percent problem “ $28$ is $80\%$ of what number?” with equation.

Answer to Problem 3CR

  $35$

Explanation of Solution

Given:

The percent problem “ $28$ is $80\%$ of what number?” .

Concept used:

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

  $\begin{array}{ccccc}\text{A}& \text{is}& B\%& \text{of}& x\\ \downarrow & \downarrow & \downarrow & \downarrow & \downarrow \\ A& =& \frac{B}{100}& ·& x\end{array}$

So, the equation becomes $A=\frac{B}{100}·x$ .

Calculation:

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

  $28=\frac{80}{100}\cdot x$ .

Now, solve the equation as follows:

  $\begin{array}{c}\text{ 28}=\frac{80}{100}\cdot x\\ 28=\frac{4}{5}\cdot x\\ 28\cdot \frac{5}{4}=\frac{5}{4}\cdot \frac{4}{5}\cdot x\text{Multiply both sides with }\frac{5}{4}\text{.}\\ 35=x\\ x=35\end{array}$

Therefore, $28$ is $80\%$ of

  $x=35$

Conclusion:

The solution of the percent problem is $35$ .