Question

A sandwich shop was willing to pay $2 to each person interviewed about the likes and dislikes of types of sandwich breads. Of the people interviewed 40 liked white bread, 75 liked wheat bread, 35 liked both, and 15 liked neither type. A. Construct a Venn diagram that illustrates the interview results.B. What is the total number of people that were interviewed. What was the total amount that the sandwich shop paid for the interviews?C. What percent of the people interviewed liked either white or wheat bread.

Answer 1

ANSWER and EXPLANATION

A. First, we have to find the number of people that liked white bread only and wheat bread only.

To find the number of people that liked white bread only, subtract the number of people that liked both from the number of people that liked white bread:

`\begin{gathered} n(white\text{ }bread\text{ }only)=40-35 \\ n(white\text{ }bread\text{ }only)=5 \end{gathered}`

To find the number of people that liked wheat bread only, subtract the number of people that liked both from the number of people that liked wheat bread:

`\begin{gathered} n(wheat\text{ }bread\text{ }only)=75-35 \\ n(wheat\text{ }bread\text{ }only)=40 \end{gathered}`

Now, we can draw the Venn diagram:

B. The total number of people interviewed is the sum of all the numbers on the Venn diagram.

Therefore, the total number of people interviewed is:

`\begin{gathered} n(total)=5+35+40+15 \\ n(total)=95 \end{gathered}`

That is the total number of people that were interviewed.

To find the total amount that the sandwich shop paid, multiply the total number of people interviewed by $2:

`\begin{gathered} Total\text{ }amount\text{ }paid=2*95 \\ Total\text{ }amount\text{ }paid=\$190 \end{gathered}`

That is the total amount that the sandwich shop paid for the interviews.

C. To find the percentage of people that liked either white bread or wheat bread, find the sum of people that liked white bread only, wheat bread only, and both types of bread, divide it by the total number of people interviewed and multiply by 100:

`\begin{gathered} \Rightarrow(5+35+40)/(95)*100 \\ \\ \Rightarrow(80)/(95)*100 \\ \\ \Rightarrow84.2\% \end{gathered}`

That is the percent of people that like either white or wheat bread.