Can anyone help me?
An 85-year-old woman in Rotorua, New Zealand, won't have to pay her library fine. A book she borrowed from the local library in 1945 was found during a move. Based on the borrowing rules pasted inside the front cover of the book, the fine should have been over $6,000. However, the library simply asked for the privilege of displaying the book that was overdue for 61 years.
Based on the following pieced of information, what is the library's daily fine?
-The total fine was $6,679.80
-The book was overdue for 61 years.
-For the first two weeks of the overdue period, there was a set fine per day.
-The second two-week of the overdue period doubled the fine per day.
-After four weeks, the fine per day was tripled.
To determine the library's daily fine, we can break down the information given and calculate it step by step.
First, we know that the total fine was $6,679.80.
Next, we know that the book was overdue for 61 years. To calculate the number of days, we multiply 61 years by 365 days per year, which equals 22,365 days.
Now, let's analyze the fines based on the provided information:
- For the first two weeks of the overdue period, there was a set fine per day.
- The second two weeks of the overdue period doubled the fine per day.
- After four weeks, the fine per day was tripled.
Let's break down the calculation into three stages:
Stage 1: Calculate the fine for the first two weeks.
Let's assume the fine per day during this period is "x."
The number of days in two weeks is 14.
So, the fine for the first two weeks would be 14 * x.
Stage 2: Calculate the fine for the next two weeks.
During this period, the fine per day is doubled, so it becomes "2x."
Since the book was overdue for 61 years (22,365 days), we have already accounted for 14 days in the previous stage. So, the remaining days for this stage would be 22,365 - 14 = 22,351 days.
Therefore, the fine for the next two weeks would be 22,351 * (2x).
Stage 3: Calculate the fine for the remaining duration after four weeks.
After four weeks, the fine per day is tripled, so it becomes "3x."
Using the same logic as before, the remaining days for this stage would be 22,351 - 14 = 22,337 days.
So, the fine for the remaining duration after four weeks would be 22,337 * (3x).
From the given information, we also know that the total fine is $6,679.80. Hence, we can set up the equation:
14x + 22,351 * (2x) + 22,337 * (3x) = $6,679.80.
By solving this equation, we can find the value of "x," which represents the fine per day.
It's important to note that this equation assumes a constant value for the fine per day within each stage (first two weeks, next two weeks, and after four weeks) but does not consider any other factors that may have influenced the final fine amount.
To find the library's daily fine, we can break down the total fine based on the given information:
1. The book was overdue for 61 years, which is equivalent to 2 weeks + 2 weeks + 57 years and 4 weeks.
2. For the first two weeks, there was a set fine per day. Let's represent this fine as "x." So, the first two weeks contribute to a fine of 14x.
3. The next two weeks, the fine per day doubled. Therefore, the second two weeks contribute to a fine of 14(2x) = 28x.
4. After four weeks, the fine per day was tripled. So, the fine per day at this point is 3x.
5. The overdue period remaining after 4 weeks is 57 years and 4 weeks, which is equivalent to 365(57) + 28 days.
Now, let's calculate the daily fine by setting up an equation based on the given information:
14x + 28x + (365(57) + 28) * 3x = $6,679.80
Simplifying the equation, we have:
42x + (365(57) + 28) * 3x = $6,679.80
Calculating the right side of the equation:
42x + (365(57) + 28) * 3x = $6,679.80
42x + (20,805 + 28) * 3x = $6,679.80
42x + 20,833 * 3x = $6,679.80
42x + 62,499x = $6,679.80
62,541x = $6,679.80
Now, we can solve for x:
x = $6,679.80 / 62,541
x ≈ $0.107
Hence, the library's daily fine is approximately $0.107.