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.
Does anyone have any idea on how to do this? I tackled it a few ways and I just can't get it.
Thanks.
To determine the library's daily fine, we need to break down the total fine and the duration of the overdue period into the different time periods with their respective fines.
First, let's determine the fine for the first two weeks of the overdue period. Since the fine per day is not mentioned, we'll need to calculate it.
Let's assume "x" represents the fine per day for the first two weeks. Assuming there are 14 days in two weeks, the total fine for this period would be:
Total fine for the first two weeks = x * 14
Next, for the next two weeks, the fine per day is doubled. So the fine per day for this period would be 2x. Assuming there are another 14 days in this period, the total fine for this period would be:
Total fine for the next two weeks = (2x) * 14
Finally, after four weeks, the fine per day is tripled. So the fine per day for this period would be 3x. Assuming the remaining overdue period is 61 - 28 = 33 years, the total fine for this period would be:
Total fine for the remaining period = (3x) * (33 * 365)
Now, we can set up an equation using the given information:
Total fine = Total fine for the first two weeks + Total fine for the next two weeks + Total fine for the remaining period
Substituting the calculated expressions, we have:
$6,679.80 = x * 14 + (2x) * 14 + (3x) * (33 * 365)
Now we can solve this equation to find the value of x, which represents the daily fine.
Simplifying the equation:
$6,679.80 = 14x + 28x + (3x) * 33 * 365
$6,679.80 = 14x + 28x + 3x * 12,045
$6,679.80 = 14x + 28x + 36,135x
$6,679.80 = 42,177x
Dividing both sides of the equation by 42,177:
x ≈ $0.158 or approximately $0.16
Therefore, the library's daily fine is approximately $0.16.