Question

Greg is selling raffle tickets at his school fundraiser. His teacher supplies him with a cashbox to collect money. To allow Greg to make change, the cashbox starts with a few dollars inside.
There is a linear relationship between the number of tickets sold and the total amount of money in the cashbox.
Number of tickets sold Total amount of money
10 $20
20 $35
30 $50
40 $65
Describe the rate of change for this relationship.
The total amount in the cashbox
by
per ticket.

Answer 1

To determine the rate of change for the relationship between the number of tickets sold and the total amount of money in the cashbox, we can analyze the given data points and calculate the change in total amount of money as the number of tickets sold increases.

Looking at the data points:

- When 10 tickets are sold, the total amount is $20.
- When 20 tickets are sold, the total amount is $35.
- When 30 tickets are sold, the total amount is $50.
- When 40 tickets are sold, the total amount is $65.

Now, we can calculate the change in total amount of money per ticket sold:

1. From 10 to 20 tickets:
- Change in total amount = $35 - $20 = $15
- Change in tickets = 20 - 10 = 10
- Rate of change = $15 / 10 tickets = $1.50 per ticket

2. From 20 to 30 tickets:
- Change in total amount = $50 - $35 = $15
- Change in tickets = 30 - 20 = 10
- Rate of change = $15 / 10 tickets = $1.50 per ticket

3. From 30 to 40 tickets:
- Change in total amount = $65 - $50 = $15
- Change in tickets = 40 - 30 = 10
- Rate of change = $15 / 10 tickets = $1.50 per ticket

The rate of change is consistent across all intervals, which suggests that the total amount of money in the cashbox increases by $1.50 for each ticket sold.

Therefore, we can conclude that the total amount in the cashbox increases by **$1.50 per ticket**.