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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 consistent across all given data points for each museum.

Let's analyze each museum step by step:

### Museum A:
- Visitors: 2 | Fee: 4 -> Ratio = [tex]\( \frac{4}{2} = 2 \)[/tex]
- Visitors: 3 | Fee: 5 -> Ratio = [tex]\( \frac{5}{3} \approx 1.6667 \)[/tex]
- Visitors: 4 | Fee: 6 -> Ratio = [tex]\( \frac{6}{4} = 1.5 \)[/tex]

The ratios are not consistent for Museum A (2, 1.6667, and 1.5), so the entrance fee is not proportional to the number of visitors.

### Museum B:
- Visitors: 1 | Fee: 2 -> Ratio = [tex]\( \frac{2}{1} = 2 \)[/tex]
- Visitors: 4 | Fee: 8 -> Ratio = [tex]\( \frac{8}{4} = 2 \)[/tex]
- Visitors: 6 | Fee: 11 -> Ratio = [tex]\( \frac{11}{6} \approx 1.8333 \)[/tex]

The ratios are not consistent for Museum B (2, 2, and 1.8333), so the entrance fee is not proportional to the number of visitors.

### Museum C:
- Visitors: 3 | Fee: 4 -> Ratio = [tex]\( \frac{4}{3} \approx 1.3333 \)[/tex]
- Visitors: 12 | Fee: 16 -> Ratio = [tex]\( \frac{16}{12} \approx 1.3333 \)[/tex]
- Visitors: 18 | Fee: 24 -> Ratio = [tex]\( \frac{24}{18} \approx 1.3333 \)[/tex]

The ratios are consistent for Museum C (all are approximately 1.3333), so the entrance fee is proportional to the number of visitors.

### Conclusion:
Museum C is the one where the entrance fee is proportional to the number of visitors.

Therefore, the correct answer is:
C. museum C

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