Chapter 7.2, Problem 21E

To determine

A real-world percent problem that can be solved by using the given proportion.

The value of $x$ in the problem.

Answer to Problem 21E

The value of $x$ in the problem is $\text{75}$ .

Explanation of Solution

Given information:

Consider the proportion given in the question:

  $\frac{30}{x}=\frac{40}{100}$

Concept used:

  $\begin{array}{l}\text{Represent }"a\text{ is }p\text{ percent of }b\text{" using the proportion}\\ \frac{a}{b}=\frac{p}{100}\\ \text{where }a\text{ is a part of the base }b\text{ and }p\text{\%,or }\frac{p}{100},\text{ is the percent}\text{.}\end{array}$

Calculation:

As per the problem

Consider, In a society $40\%\text{ of the residents are children}\text{.}$

The number of children in the society is $30$ .

Find the total number of residents of the society.

Consider the total number of residents in the society as $x$

Write the proportion

  $\frac{a}{b}=\frac{p}{100}$

Substitute $\text{30 for }a\text{, }x\text{ for }b\text{ and 40 for }p\text{.}$

  $\frac{30}{x}=\frac{40}{100}$

Use cross product property

  $\text{100}\cdot 30=40\cdot x$

Multiply

  $3000=40x$

Divide both sides by $40$ and simplify

  $\text{75}=x$

Therefore,

The total number of residents in the society is $\text{75}$ .

Hence,

The value of $x$ in the problem is $\text{75}$ .