Chapter 6, Problem 12CR

To determine

The solution of the percent problem “what is $33\frac{1}{3}\%$ of $27$ ?” with equation.

Answer to Problem 12CR

  $9$

Explanation of Solution

Given:

The percent problem “what is $33\frac{1}{3}\%$ of $27$ ?”.

Concept used:

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

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

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

Calculation:

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

  $x=33\frac{1}{3}\cdot \frac{1}{100}\cdot 27$ .

Now, solve the equation as follows:

  $\begin{array}{c}x=33\frac{1}{3}\cdot \frac{1}{100}\cdot 27\\ x=\frac{100}{3}\cdot \frac{1}{100}\cdot 27\\ x=9\end{array}$

Therefore, the number which is $33\frac{1}{3}\%$ of $27$ is

  $x=9$

Conclusion:

The solution of the percent problem is $9$ .