Question
Days- 2/ Fine- 30 cents/ Days- 3/ Fine- 45 cents/ Days- 4/ Fine- 60 cents. The table shows the fine owed for an overdue library book according to how many days it is overdue. What is the initial value?
Answers
GPT-4o mini
In the given table, the fines for the overdue library book based on the number of days overdue are:
- For 2 days, the fine is 30 cents.
- For 3 days, the fine is 45 cents.
- For 4 days, the fine is 60 cents.
To find the initial value (the fine for 0 days overdue), we can observe the pattern in the fines. The fine increases consistently as the number of overdue days increases.
Calculating the fines per day:
- From day 2 to day 3 (1 day): The fine increases from 30 cents to 45 cents, which is an increase of 15 cents.
- From day 3 to day 4 (1 day): The fine increases from 45 cents to 60 cents, which is also an increase of 15 cents.
This indicates that the fine increases by 15 cents for each additional day overdue.
We can find the initial value (0 days overdue) by working backwards from the known fine for 2 days (30 cents):
- For 1 day overdue, the fine would be \(30 \, \text{cents} - 15 \, \text{cents} = 15 \, \text{cents}\).
- For 0 days overdue, the fine would be \(15 \, \text{cents} - 15 \, \text{cents} = 0 \, \text{cents}\).
Thus, the initial value (fine owed for 0 days overdue) is **0 cents**.
- For 2 days, the fine is 30 cents.
- For 3 days, the fine is 45 cents.
- For 4 days, the fine is 60 cents.
To find the initial value (the fine for 0 days overdue), we can observe the pattern in the fines. The fine increases consistently as the number of overdue days increases.
Calculating the fines per day:
- From day 2 to day 3 (1 day): The fine increases from 30 cents to 45 cents, which is an increase of 15 cents.
- From day 3 to day 4 (1 day): The fine increases from 45 cents to 60 cents, which is also an increase of 15 cents.
This indicates that the fine increases by 15 cents for each additional day overdue.
We can find the initial value (0 days overdue) by working backwards from the known fine for 2 days (30 cents):
- For 1 day overdue, the fine would be \(30 \, \text{cents} - 15 \, \text{cents} = 15 \, \text{cents}\).
- For 0 days overdue, the fine would be \(15 \, \text{cents} - 15 \, \text{cents} = 0 \, \text{cents}\).
Thus, the initial value (fine owed for 0 days overdue) is **0 cents**.