Questions: Constructing a Venn diagram with 2 sets to solve a word problem A college radio station surveyed 132 incoming freshmen to gather information about the genres of music that they like. The table below gives the results for two of the genres. - Number of freshmen - Like rap: 66 - Like jazz: 85 - Like both rap and jazz: 47 Construct a Venn diagram illustrating these results. Then answer the questions. How many freshmen like jazz but not rap? 38 freshmen How many freshmen like rap or jazz (or both)? 104 freshmen

Constructing a Venn diagram with 2 sets to solve a word problem A college radio station surveyed 132 incoming freshmen to gather information about the genres of music that they like. The table below gives the results for two of the genres. - Number of freshmen - Like rap: 66 - Like jazz: 85 - Like both rap and jazz: 47 Construct a Venn diagram illustrating these results. Then answer the questions. How many freshmen like jazz but not rap? 38 freshmen How many freshmen like rap or jazz (or both)? 104 freshmen
Transcript text: Constructing a Venn diagram with 2 sets to solve a word problem A college radio station surveyed 132 incoming freshmen to gather information about the genres of music that they like. The table below gives the results for two of the genres. \begin{tabular}{|c|c|} \cline { 2 - 2 } \multicolumn{1}{c|}{} & Number of freshmen \\ \hline Like rap & 66 \\ \hline Like jazz & 85 \\ \hline Like both rap and jazz & 47 \\ \hline \end{tabular} Construct a Venn diagram illustrating these results. Then answer the questions. How many freshmen like jazz but not rap? 38 freshmen How many freshmen like rap or jazz (or both)? 104 freshmen
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Solution

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Solution Steps

To solve this problem, we need to first construct a Venn diagram with two sets representing the genres of music (rap and jazz) and the intersection between them. Then, we can use the information provided in the table to fill in the appropriate values in the diagram. Once the Venn diagram is constructed, we can easily determine the number of freshmen who like jazz but not rap and the total number of freshmen who like rap or jazz (or both).

Step 1: Calculate the total number of freshmen surveyed

Total number of freshmen surveyed = Number who like rap + Number who like jazz - Number who like both rap and jazz Total number of freshmen surveyed = 66 + 85 - 47 Total number of freshmen surveyed = 104

Step 2: Calculate the number of freshmen who like jazz but not rap

Number of freshmen who like jazz but not rap = Total number who like jazz - Number who like both rap and jazz Number of freshmen who like jazz but not rap = 85 - 47 Number of freshmen who like jazz but not rap = 38

Step 3: Calculate the number of freshmen who like rap or jazz (or both)

Number of freshmen who like rap or jazz (or both) = Total number of freshmen surveyed Number of freshmen who like rap or jazz (or both) = 104

Final Answer

The number of freshmen who like jazz but not rap is $\boxed{38}$ and the number of freshmen who like rap or jazz (or both) is $\boxed{104}$.

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