Chapter 7.2, Problem 22E

a.

To determine

The percentage of students surveyed who prefer summer; fall.

Answer to Problem 22E

Percent of students surveyed who prefer summer = $50\%$

Percent of students surveyed who prefer fall = $12.5\%$

Explanation of Solution

Given:

Middle schools students are surveyed to know their preference of season for holding school trip.

The bar graph given in the question:

  

Calculation:

As per the problem

Consider the bar graph,

  

Number of students surveyed who prefer winter = $\text{27}$

Number of students surveyed who prefer spring = $\text{108}$

Number of students surveyed who prefer summer = $\text{180}$

Number of students surveyed who prefer fall = $\text{45}$

Total number of students surveyed = $\text{27+108+180 +45=360}$

Percent of students surveyed who prefer summer $=\frac{\text{number of students who prefer summer}}{\text{total number of students surveyed}}\times 100$ $=\frac{180}{360}\times 100=50\%$ [Put the values and simplify]

Percent of students surveyed who prefer summer $=\frac{\text{number of students who prefer fall}}{\text{total number of students surveyed}}\times 100$ $=\frac{45}{360}\times 100=12.5\%$ [Put the values and simplify]

Hence,

Percent of students surveyed who prefer summer = $50\%$

Percent of students surveyed who prefer fall = $12.5\%$

Conclusion:

Percent of students surveyed who prefer summer = $50\%$

Percent of students surveyed who prefer fall = $12.5\%$

b.

To determine

The number of $\text{8th}$ graders who prefer spring.

Answer to Problem 22E

The number of $\text{8th}$ graders who prefer spring is $81$ .

Explanation of Solution

Given:

Number of students surveyed who prefer spring = $\text{108}$

  $\text{75\%}$ of students who prefer spring are $\text{8th}$ graders.

Calculation:

As per the given problem

Number of students who prefer spring = $\text{108}$

Percent of students who are $\text{8th}$ graders = $\text{75\%}$

To find $\text{75\%}$ of $\text{108}$ , use the fact $\text{75\%=}\frac{75}{100}=\frac{3}{4}$ . Then multiply,

  $\begin{array}{l}\text{75\% of 108 =}\frac{3}{4}\cdot 108\left[\text{write percent as a fraction}\right]\\ \Rightarrow \frac{324}{4}=81\text{ [multiply and simplify]}\end{array}$

Hence,

  $81\text{ students among 108 are 8th graders}\text{.}$

Conclusion:

The number of $\text{8th}$ graders who prefer spring is $81$ .

c.

To determine

The number of students who would prefer a school trip in spring.

Answer to Problem 22E

The total students in the school who would prefer school trip in spring is $234.$

Explanation of Solution

Given:

Total number of students in the school = $780$

Number of students surveyed who prefer spring = $\text{108}$

Calculation:

As per the given problem

Total number of students in the school = $780$

Number of students surveyed who prefer spring = $\text{108}$

Total number of students surveyed = $360$

Percent of students surveyed who prefer spring $=\frac{\text{number of students who prefer spring}}{\text{total number of students surveyed}}\times 100$

= $\frac{108}{360}\times 100=30\%$

Since $30\%$ of the students surveyed prefer spring for school trip,

Assume $30\%$ of the total students would prefer school trip in spring.

Therefore,

The number of students who would prefer school trip in spring = $30\%\text{ of 780}$ $=\frac{30}{100}\times 780$ $=234.$

Hence,

The total students in the school who would prefer school trip in spring $=234.$

Conclusion:

The total students in the school who would prefer school trip in spring is $234.$