Select the correct answer.
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?
| Visitors | Fee ($) | Visitors | Fee ($) | Visitors | Fee ($) |
|---|---|---|---|---|---|
| 2 | 4 | 1 | 2 | 3 | 4 |
| 3 | 5 | 4 | 8 | 12 | 16 |
| 4 | 6 | 6 | 11 | 18 | 24 |
A. museum A
B. museum B
C. museum C
D. museum A and museum B
Answer (2)
After analyzing the entrance fees for each museum, Museum C has a constant ratio of fee to visitors, indicating a proportional relationship. Therefore, the entrance fee is proportional to the number of visitors at Museum C. The correct answer is C.
;
Calculate the ratio of fee to visitors for Museum A: The ratios are not constant.
Calculate the ratio of fee to visitors for Museum B: The ratios are not constant.
Calculate the ratio of fee to visitors for Museum C: The ratios are constant.
Conclude that Museum C has an entrance fee proportional to the number of visitors: C .
Explanation
Analyzing the Problem Let's analyze the entrance fees for each museum to determine which one has a fee proportional to the number of visitors. A proportional relationship means that the ratio of the fee to the number of visitors is constant.
Museum A Analysis For Museum A, we have the following data points:
2 visitors: $4
3 visitors: $5
4 visitors: $6 Let's calculate the ratios of fee to visitors for each data point:
Ratio 1: 2 4 = 2
Ratio 2: 3 5 ≈ 1.67
Ratio 3: 4 6 = 1.5 Since the ratios are not equal, Museum A's entrance fee is not proportional to the number of visitors.
Museum B Analysis For Museum B, we have the following data points:
1 visitor: $2
4 visitors: $8
6 visitors: $11 Let's calculate the ratios of fee to visitors for each data point:
Ratio 1: 1 2 = 2
Ratio 2: 4 8 = 2
Ratio 3: 6 11 ≈ 1.83 Since the ratios are not equal, Museum B's entrance fee is not proportional to the number of visitors.
Museum C Analysis For Museum C, we have the following data points:
3 visitors: $4
12 visitors: $16
18 visitors: $24 Let's calculate the ratios of fee to visitors for each data point:
Ratio 1: 3 4 ≈ 1.33
Ratio 2: 12 16 = 3 4 ≈ 1.33
Ratio 3: 18 24 = 3 4 ≈ 1.33 Since the ratios are equal, Museum C's entrance fee is proportional to the number of visitors.
Conclusion Based on our analysis, Museum C has an entrance fee proportional to the number of visitors.
Examples
Understanding proportional relationships is useful in many real-life situations. For example, if you are buying apples at a store, the cost is usually proportional to the weight of the apples you buy. If 1 kg of apples costs $2, then 2 kg of apples will cost $4, and so on. This concept is also used in cooking, where the amount of ingredients is proportional to the number of servings you want to make. If a recipe for 4 servings requires 1 cup of flour, then a recipe for 8 servings will require 2 cups of flour.
