Chapter 10.7, Problem 8IP

a.

To determine

To predict: The number of votes Carlos would receive.

Answer to Problem 8IP

Carlos would receive $104$ votes.

Explanation of Solution

Given Information: Information from a previous survey and total students are $520$ .

Calculation:

Total number of responses in previous survey $=5+6+12+9+16+12=60$

Number of votes Carlos received in previous survey $=12$

Let Carlos would receive $n$ number of votes.

Using percentage proportion to calculate the required number,

  $\begin{array}{l}\frac{n}{520}=\frac{12}{60}\\ \\ \Rightarrow n\times 60=6240(Cross-product)\\ \\ \Rightarrow n=104\end{array}$

Thus, Carlos would receive $104$ votes.

b.

To determine

To predict: The difference between number of votes Ming and Jack would receive.

Answer to Problem 8IP

Ming would receive $26$ more votes than Jack.

Explanation of Solution

Given Information: Information from a previous survey and total students are $520$ .

Calculation:

Total number of responses in previous survey $=5+6+12+9+16+12=60$

Number of votes Ming received in previous survey $=12$

Number of votes Jack received in previous survey $=9$

Let $n_1$ and $n_2$ be the number of votes that Ming and Jack would receive respectively.

Using percentage proportion to calculate number of votes Ming would receive, $\begin{array}{l}\frac{n_1}{520}=\frac{12}{60}\\ \\ \Rightarrow n_1\times 60=6240(Cross-product)\\ \\ \Rightarrow n_1=104\end{array}$

Using percentage proportion to calculate number of votes Jack would receive,

  $\begin{array}{l}\frac{n_2}{520}=\frac{9}{60}\\ \\ \Rightarrow n_2\times 60=4680(Cross-product)\\ \\ \Rightarrow n_2=78\end{array}$

Difference between number of votes that Ming and Jack would receive $=n_1-n_2=104-78=26$ .

Thus, Ming would receive $26$ more votes than Jack.