Chapter 6, Problem 22CR

To determine

The solution of the percent problem “ $55$ is $20\%$ of what number?” with equation.

Answer to Problem 22CR

  $275$

Explanation of Solution

Given:

The percent problem “ $55$ is $20\%$ 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 number is $x$ . 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

  $55=\frac{20}{100}\cdot x$ .

Now, solve the equation as follows:

  $\begin{array}{c}\text{ 55}=\frac{20}{100}\cdot x\\ \text{55}=\frac{1}{5}\cdot x\\ 55\cdot 5=5\cdot \frac{1}{5}\cdot x\text{Multiply both sides with 5}\text{.}\\ 275=x\\ x=275\end{array}$

Therefore, $55$ is $20\%$ of $x=275.$

Conclusion:

The solution of the percent problem is $275$ .