Chapter 6, Problem 9CR

To determine

To find the total number students in the class.

Answer to Problem 9CR

  $42$

Explanation of Solution

Given:

30 is 70% of total students in the class.

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

  $30=\frac{70}{100}\cdot x$ .

Now, solve the equation as follows:

  $\begin{array}{c}\text{ 30}=\frac{70}{100}\cdot x\\ 30=\frac{7}{10}\cdot x\\ 30\cdot \frac{10}{7}=\frac{10}{7}\cdot \frac{7}{10}\cdot x\text{Multiply both sides with }\frac{10}{7}\text{.}\\ \frac{300}{7}=x\\ x=42\end{array}$

Therefore, total number of students in the class is

  $x=42$

Conclusion:

The solution of the percent problem is $42$ .