Question
Use the table to answer the question.
Cost of Tickets Based on the Number of Adults Attending
Number of Adults 1 2 3 5 10 100
Cost of Tickets ($) 75 150 225 375 750 7,500
Determine if the quantities in the data table are in a proportional relationship. If the quantities have a proportional relationship, answer 1. If the quantities do not have a proportional relationship, answer 2.
Cost of Tickets Based on the Number of Adults Attending
Number of Adults 1 2 3 5 10 100
Cost of Tickets ($) 75 150 225 375 750 7,500
Determine if the quantities in the data table are in a proportional relationship. If the quantities have a proportional relationship, answer 1. If the quantities do not have a proportional relationship, answer 2.
Answers
GPT-4o mini
To determine if the quantities in the data table are in a proportional relationship, we need to see if the ratio of the cost of tickets to the number of adults is constant.
We can calculate the cost per adult for each given number of adults:
1. For 1 adult:
\(\frac{75}{1} = 75\)
2. For 2 adults:
\(\frac{150}{2} = 75\)
3. For 3 adults:
\(\frac{225}{3} = 75\)
4. For 5 adults:
\(\frac{375}{5} = 75\)
5. For 10 adults:
\(\frac{750}{10} = 75\)
6. For 100 adults:
\(\frac{7500}{100} = 75\)
In each case, the cost per adult is consistently \(75\). Since the ratio of the cost to the number of adults is constant, the quantities in the data table are in a proportional relationship.
The answer is **1**.
We can calculate the cost per adult for each given number of adults:
1. For 1 adult:
\(\frac{75}{1} = 75\)
2. For 2 adults:
\(\frac{150}{2} = 75\)
3. For 3 adults:
\(\frac{225}{3} = 75\)
4. For 5 adults:
\(\frac{375}{5} = 75\)
5. For 10 adults:
\(\frac{750}{10} = 75\)
6. For 100 adults:
\(\frac{7500}{100} = 75\)
In each case, the cost per adult is consistently \(75\). Since the ratio of the cost to the number of adults is constant, the quantities in the data table are in a proportional relationship.
The answer is **1**.