To determine which museum's entrance fee is proportional to the number of visitors, we need to check if the fee per visitor remains constant across different visitor counts. Here is the step-by-step analysis for each museum:
### Museum A:
Visitors and corresponding fees:
- 2 visitors, [tex]$4 fee
- 3 visitors, $[/tex]5 fee
- 4 visitors, [tex]$6 fee
Now, calculate the fee per visitor for Museum A:
\[
\text{For 2 visitors} \rightarrow \frac{4}{2} = 2
\]
\[
\text{For 3 visitors} \rightarrow \frac{5}{3} \approx 1.67
\]
\[
\text{For 4 visitors} \rightarrow \frac{6}{4} = 1.5
\]
The fee per visitor is not consistent for Museum A: \(2\), \(1.67\), and \(1.5\) are different values. So, the fees are not proportional to the number of visitors.
### Museum B:
Visitors and corresponding fees:
- 1 visitor, $[/tex]2 fee
- 4 visitors, [tex]$8 fee
- 6 visitors, $[/tex]11 fee
Now, calculate the fee per visitor for Museum B:
[tex]\[
\text{For 1 visitor} \rightarrow \frac{2}{1} = 2
\][/tex]
[tex]\[
\text{For 4 visitors} \rightarrow \frac{8}{4} = 2
\][/tex]
[tex]\[
\text{For 6 visitors} \rightarrow \frac{11}{6} \approx 1.83
\][/tex]
Again, the fee per visitor is not consistent for Museum B: [tex]\(2\)[/tex], [tex]\(2\)[/tex], and [tex]\(1.83\)[/tex] are different values. So, the fees are not proportional to the number of visitors.
### Museum C:
Visitors and corresponding fees:
- 3 visitors, [tex]$4 fee
- 12 visitors, $[/tex]16 fee
- 18 visitors, $24 fee
Now, calculate the fee per visitor for Museum C:
[tex]\[
\text{For 3 visitors} \rightarrow \frac{4}{3} \approx 1.33
\][/tex]
[tex]\[
\text{For 12 visitors} \rightarrow \frac{16}{12} \approx 1.33
\][/tex]
[tex]\[
\text{For 18 visitors} \rightarrow \frac{24}{18} \approx 1.33
\][/tex]
The fee per visitor is consistent for Museum C: [tex]\( \approx 1.33\)[/tex] for each case. Hence, the fees are proportional to the number of visitors.
Therefore, the museum where the entrance fee is proportional to the number of visitors is:
C. Museum C
