Chapter 6, Problem 5CR

To determine

The solution of the percent problem “what distance is $72\%$ of $120$ miles?” with equation.

Answer to Problem 5CR

  $86.4$

Explanation of Solution

Given:

The percent problem “what distance is $72\%$ of $120$ miles?”.

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

  $x=72\cdot \frac{1}{100}\cdot 120$ .

Now, solve the equation as follows:

  $\begin{array}{c}x=72\cdot \frac{1}{100}\cdot 120\\ x=\frac{864}{10}\\ x=86.4\end{array}$

Therefore, the distance which is $72\%$ of $120$ miles is

  $x=86.4$

Conclusion:

The solution of the percent problem is $86.4$ .