Let's analyze the problem step by step to determine the correct answer.
The table provides the number of visitors and the fee charged by three different museums, A, B, and C. Our objective is to determine whether the entrance fee is proportional to the number of visitors for each museum.
For a relationship to be proportional, the ratio of the fee to the number of visitors should remain constant for all data points provided.
### Museum A:
- Visitors: 2, 3, 4
- Fees: [tex]$4, $[/tex]5, [tex]$6
Calculate the ratio of fee to visitors for each entry:
1. \( \frac{4}{2} = 2.0 \)
2. \( \frac{5}{3} \approx 1.6667 \)
3. \( \frac{6}{4} = 1.5 \)
The ratios are not consistent (2.0, 1.6667, 1.5). Therefore, the fees at Museum A are not proportional to the number of visitors.
### Museum B:
- Visitors: 1, 4, 6
- Fees: $[/tex]2, [tex]$8, $[/tex]11
Calculate the ratio of fee to visitors for each entry:
1. [tex]\( \frac{2}{1} = 2.0 \)[/tex]
2. [tex]\( \frac{8}{4} = 2.0 \)[/tex]
3. [tex]\( \frac{11}{6} \approx 1.8333 \)[/tex]
The ratios are not consistent (2.0, 2.0, 1.8333). Therefore, the fees at Museum B are not proportional to the number of visitors.
### Museum C:
- Visitors: 3, 12, 18
- Fees: [tex]$4, $[/tex]16, $24
Calculate the ratio of fee to visitors for each entry:
1. [tex]\( \frac{4}{3} \approx 1.3333 \)[/tex]
2. [tex]\( \frac{16}{12} \approx 1.3333 \)[/tex]
3. [tex]\( \frac{24}{18} \approx 1.3333 \)[/tex]
The ratios are consistent (1.3333, 1.3333, 1.3333). Therefore, the fees at Museum C are proportional to the number of visitors.
Since only Museum C has a consistent ratio, the correct answer is:
C. museum C
