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Select the correct answer.

A high school surveyed students to determine if new foreign language classes should be added to the course offerings for the next school year. The two-way frequency table below shows the interest of next year's underclassmen in the new courses.

\begin{tabular}{|c|c|c|c|c|}
\hline & German & Mandarin & Neither & Total \\
\hline Freshmen & 30 & 80 & 230 & 340 \\
\hline Sophomores & 15 & 65 & 200 & 280 \\
\hline Total & 45 & 145 & 430 & 620 \\
\hline
\end{tabular}

Approximately what percentage of the underclassmen have an interest in taking a Mandarin course next year?

A. [tex]$23.39 \%$[/tex]
B. [tex]$44.83 \%$[/tex]
C. [tex]$33.72 \%$[/tex]
D. [tex]$55.17 \%$[/tex]



Answer :

GinnyAnswer
To determine the percentage of underclassmen interested in taking a Mandarin course next year, follow these steps:

1. Identify the total number of underclassmen surveyed: According to the table, the total number is given in the bottom right corner:
[tex]\[ \text{Total number of underclassmen} = 620 \][/tex]

2. Identify the number of underclassmen interested in taking Mandarin course: This number is provided in the table's second column's bottom cell:
[tex]\[ \text{Number of students interested in Mandarin} = 145 \][/tex]

3. Calculate the percentage of students interested in Mandarin: Use the formula for percentage:
[tex]\[ \text{Percentage} = \left(\frac{\text{Number of students interested in Mandarin}}{\text{Total number of underclassmen}}\right) \times 100 \][/tex]

4. Perform the calculation:
[tex]\[ \text{Percentage} = \left(\frac{145}{620}\right) \times 100 \][/tex]

This results in approximately:
[tex]\[ 23.387096774193548\% \][/tex]

5. Choose the closest answer:
[tex]\[ 23.39\% \][/tex]

Therefore, the correct answer is:
[tex]\[ \boxed{23.39\%} \][/tex]

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