Question

Use the table to answer the question.

Calculating the initial fine amount by the number of outstanding days.
Days Fine
2 30 cents
3 45 cents
4 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?

Answer 1

To find the initial value (the fine amount for the first day a book is overdue), we can look for a pattern in the fines listed in the table. We see that the fines increase as the number of overdue days increases.

Let's analyze the fines provided:

- For 2 days: 30 cents
- For 3 days: 45 cents
- For 4 days: 60 cents

We can calculate the amount added for each additional day:

- From 2 to 3 days (1 additional day): 45 cents - 30 cents = 15 cents
- From 3 to 4 days (1 additional day): 60 cents - 45 cents = 15 cents

The fine increases by 15 cents for each additional day overdue.

Let \( x \) be the fine for the first day (Day 1).

If we assume that the fine for the first day is \( x \), then:
- After 2 days, the fine would be \( x + 15 \) (for Day 1 and Day 2)
- After 3 days, the fine would be \( x + 30 \) (for Day 1, Day 2, and Day 3)
- After 4 days, the fine would be \( x + 45 \) (for Day 1, Day 2, Day 3, and Day 4)

From the table:
- When overdue for 2 days: \( x + 15 = 30 \)
- So, \( x = 30 - 15 = 15 \) cents for the first day.

Thus, the initial fine value for the first day is **15 cents**.