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Three museums charge an entrance fee based on the number of visitors in the group. The table lists the fees charged by the museums. At which museum is the entrance fee proportional to the number of visitors?

\begin{tabular}{|r|r|r|r|r|r|}
\hline \multicolumn{2}{|c|}{ Museum A } & \multicolumn{2}{|c|}{ Museum B } & \multicolumn{2}{|c|}{ Museum C } \\
\hline Visitors & Fee (\[tex]$) & Visitors & Fee (\$[/tex]) & Visitors & Fee (\$) \\
\hline 2 & 4 & 1 & 2 & 3 & 4 \\
\hline 3 & 5 & 4 & 8 & 12 & 16 \\
\hline 4 & 6 & 6 & 11 & 18 & 24 \\
\hline
\end{tabular}

A. Museum A
B. Museum B
C. Museum C
D. Museum A and Museum B



Answer :

GinnyAnswer
To determine which museum's entrance fee is proportional to the number of visitors, we need to check if the ratio of the fee to the number of visitors is constant for each museum. Let's examine each museum one by one.

Museum A:
- For 2 visitors, the fee is \[tex]$4. The ratio is \( \frac{4}{2} = 2 \). - For 3 visitors, the fee is \$[/tex]5. The ratio is [tex]\( \frac{5}{3} \approx 1.67 \)[/tex].
- For 4 visitors, the fee is \[tex]$6. The ratio is \( \frac{6}{4} = 1.5 \). Since the ratio of fee per visitor is not constant (2, 1.67, 1.5), the entrance fee at Museum A is not proportional to the number of visitors. Museum B: - For 1 visitor, the fee is \$[/tex]2. The ratio is [tex]\( \frac{2}{1} = 2 \)[/tex].
- For 4 visitors, the fee is \[tex]$8. The ratio is \( \frac{8}{4} = 2 \). - For 6 visitors, the fee is \$[/tex]11. The ratio is [tex]\( \frac{11}{6} \approx 1.83 \)[/tex].

Since the ratio of fee per visitor is not constant (2, 2, 1.83), the entrance fee at Museum B is not proportional to the number of visitors.

Museum C:
- For 3 visitors, the fee is \[tex]$4. The ratio is \( \frac{4}{3} \approx 1.33 \). - For 12 visitors, the fee is \$[/tex]16. The ratio is [tex]\( \frac{16}{12} = \frac{4}{3} \approx 1.33 \)[/tex].
- For 18 visitors, the fee is \$24. The ratio is [tex]\( \frac{24}{18} = \frac{4}{3} \approx 1.33 \)[/tex].

Since the ratio of fee per visitor is constant ([tex]\(\frac{4}{3}\)[/tex]), the entrance fee at Museum C is proportional to the number of visitors.

Therefore, the correct answer is:
C. museum C

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