Chapter 6, Problem 6CR

To determine

The solution of the percent problem “ $36$ pounds is $15\%$ of what weight?” with equation.

Answer to Problem 6CR

  $240$ pounds

Explanation of Solution

Given:

The percent problem “ $36$ pounds is $15\%$ of what weight?”.

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

  $36=\frac{15}{100}\cdot x$ .

Now, solve the equation as follows:

  $\begin{array}{c}\text{ 36}=\frac{15}{100}\cdot x\\ 36=\frac{3}{20}\cdot x\\ 36\cdot \frac{20}{3}=\frac{20}{3}\cdot \frac{3}{20}\cdot x\text{Multiply both sides with }\frac{20}{3}\text{.}\\ 240=x\\ x=240\end{array}$

Therefore, $36$ pounds is $15\%$ of

  $x=240$

Conclusion:

The solution of the percent problem is $240$ pounds.