Chapter 7.1, Problem 57E

a.

To determine

The number of students who chose either record stores or other stores.

Answer to Problem 57E

The number of students that purchase from either record stores or other stores is $\text{648}$ .

Explanation of Solution

Given:

The given table shows the results of a class survey that asked students where they make most of their music purchases.

  

Calculation:

As per the given problem

Consider the given table

  

Total number of students surveyed = $800$

Percent of students that purchase from record stores = $45\%$

Percent of students that purchase from other stores = $36\%$

Number of students that purchase from record stores = percent of students that purchase from record stores $\times$ total number of students

  $\begin{array}{l}=45\%\cdot 800\\ =\frac{45}{100}\cdot 800\text{ [write percent as fraction]}\\ \text{=360}\end{array}$

Similarly, Number of students that purchase from other stores=percent of students that purchase from other stores $\times$ total number of students

  $\begin{array}{l}=36\%\cdot 800\\ =\frac{36}{100}\cdot 800\text{ [write percent as fraction]}\\ \text{=288}\end{array}$

Therefore,

Total number of students that purchase from either record stores or other stores

  $\begin{array}{l}\text{=360+288}\\ \text{=648}\end{array}$

Conclusion:

The number of students that purchase from either record stores or other stores is $\text{648}$ .

b.

To determine

To estimate how many more students chose record stores than music clubs

Answer to Problem 57E

  $\text{288}$ more students chose record stores than music clubs.

Explanation of Solution

Given:

The given table:

  

Total number of students surveyed = $800$

Number of students that purchase from record stores = $\text{360}$ (calculated in part (a.))

Calculation:

As per the given problem

Total number of students surveyed = $800$

Number of students that purchase from record stores = $\text{360}$

Percent of students that purchase from music clubs = $9\%$

Number of students that purchase from record stores = percent of students that purchase from music clubs

  $\times$ total number of students

  $\begin{array}{l}=9\%\cdot 800\\ =\frac{9}{100}\cdot 800\text{ [write percent as fraction]}\\ \text{=72}\end{array}$

Difference between the number of students that purchase from record stores and that from music clubs = $\text{=360-72=288}$

Conclusion:

  $\text{288}$ more students chose record stores than music clubs.

c.

To determine

To estimate how many students in both the surveys combined make most of their purchase from internet.

Answer to Problem 57E

  $\text{73}$ students in both the surveys combined make most of their purchase from internet.

Explanation of Solution

Given:

The given table:

  

Total number of students in the first survey = $800$

Percent of students that purchase from the internet in the first survey = $8\%$

Number of students surveyed in the second time = $\text{100}$

Percent of students that purchase from the internet in the second survey = $9\%$

Calculation:

As per the given problem

Total number of students in the first survey = $800$

Percent of students that purchase from the internet in the first survey = $8\%$

Number of students surveyed in the second time = $\text{100}$

Percent of students that purchase from the internet in the second survey = $9\%$

Number of students that purchase from the internetin the first survey = percent of students that purchase from internet $\times$ total number of students

  $\begin{array}{l}=8\%\cdot 800\\ =\frac{8}{100}\cdot 800\text{ [write percent as fraction]}\\ \text{=64}\end{array}$

Number of students that purchase from the internet in the secondsurvey = percent of students that purchase from internet $\times$ total number of students

  $\begin{array}{l}=9\%\cdot 100\\ =\frac{9}{100}\cdot 100\text{ [write percent as fraction]}\\ \text{=9}\end{array}$

Therefore,

Total number of students in both the surveys combined make most of their purchase from internet $\text{=64+9=73}$

Conclusion:

  $\text{73}$ students in both the surveys combined make most of their purchase from internet.