Question
A movie ticket costs $7.50 per person. Determine if the relationship between number of tickets, x, and total cost, y, is proportional. Explain how you know.
Answers
GPT 3.5
To determine if the relationship between the number of tickets, x, and the total cost, y, is proportional, we need to check if the ratio of y to x remains constant.
If the relationship is proportional, the ratio of y to x should always be the same.
Let's consider different scenarios:
Scenario 1: 1 ticket
- Number of tickets, x = 1
- Total cost, y = $7.50 (1 ticket * $7.50 per ticket)
- Ratio of y to x = 7.50/1 = 7.50
Scenario 2: 2 tickets
- Number of tickets, x = 2
- Total cost, y = $15 (2 tickets * $7.50 per ticket)
- Ratio of y to x = 15/2 = 7.50
Scenario 3: 3 tickets
- Number of tickets, x = 3
- Total cost, y = $22.50 (3 tickets * $7.50 per ticket)
- Ratio of y to x = 22.50/3 = 7.50
As we can see from the different scenarios, the ratio of y to x remains constant at 7.50. Therefore, the relationship between the number of tickets, x, and the total cost, y, is indeed proportional.
If the relationship is proportional, the ratio of y to x should always be the same.
Let's consider different scenarios:
Scenario 1: 1 ticket
- Number of tickets, x = 1
- Total cost, y = $7.50 (1 ticket * $7.50 per ticket)
- Ratio of y to x = 7.50/1 = 7.50
Scenario 2: 2 tickets
- Number of tickets, x = 2
- Total cost, y = $15 (2 tickets * $7.50 per ticket)
- Ratio of y to x = 15/2 = 7.50
Scenario 3: 3 tickets
- Number of tickets, x = 3
- Total cost, y = $22.50 (3 tickets * $7.50 per ticket)
- Ratio of y to x = 22.50/3 = 7.50
As we can see from the different scenarios, the ratio of y to x remains constant at 7.50. Therefore, the relationship between the number of tickets, x, and the total cost, y, is indeed proportional.