Chapter SH, Problem 7.10MPS

To determine

To calculate: To find how many more people aged 18-34 listen to podcasts than people aged 45 or older

Answer to Problem 7.10MPS

  $105$ morepeople aged 18-34 listen to podcasts than people aged 45 or older

Explanation of Solution

Given information: The circle graph showing the result of a survey about the ages of people who listen to podcasts and $1500$ people were surveyed

  

Formula Used:

Portion is circle graph is calculated

  $TypeA=\frac{Portion}{Total}\times 100$

Calculation:

Given the circle graph as follows:

  

Also, $1500$ people were surveyed

Number of people aged 18-34 who listen to podcast is calculated as

  $\begin{array}{l}{\%}_{18-34}=\frac{N_{18-34}}{Total}\times 100\\ \left(12+24\right)=\frac{N_{18-34}}{1500}\times 100\\ 35=\frac{N_{18-34}}{1500}\times 100\\ N_{18-34}=\frac{36\times 1500}{100}\\ N_{18-34}=36\times 15\\ N_{18-34}=540\end{array}$

Number of people aged 45 or older who listen to podcast is calculated as

  $\begin{array}{l}{\%}_{18-34}=\frac{N_{45+}}{Total}\times 100\\ \left(16+9+4\right)=\frac{N_{45+}}{1500}\times 100\\ 29=\frac{N_{45+}}{1500}\times 100\\ N_{45+}=\frac{29\times 1500}{100}\\ N_{45+}=29\times 15\\ N_{45+}=435\end{array}$

Thus, number of more people aged 18-34 who listen podcasts than people aged 45+

  $\begin{array}{l}More=540-435\\ More=105\end{array}$

Conclusion:

Hence, $105$ more people aged 18-34 listen to podcasts than people aged 45 or older