Problem Solving

A certain library assesses fines for overdue books as follows. On the first day that a book is overdue, the total fine is $0.10. For each additional day that the book is overdue, the total fine is either increased by 30 cents or doubled, whichever results in the lesser amount. What is the total fine for a book on the fourth day it is overdue?

A. $0.60
B. $0.70
C. $0.80
D. $0.90
E. $1.00

1st day - $0.10

2nd day - $0.20 or $0.40 (double or add $0.30)
$0.20 is the lesser amount

3rd day - $0.40 or $0.50 (double or add $0.30)
$0.40 is the lesser amount

4th day - $0.80 or $0.70 (double or add $0.30)
[spoiler]$0.70[/spoiler] is the lesser amount

The correct answer is B

Cheers,
Brent

sanju09 wrote:A certain library assesses fines for overdue books as follows:

On the first day that a book is overdue, the total fine is $0.10.

For each additional day that the book is overdue the total fine is either increased by $0.30 or double, whichever results in the lesser amount.

What is the total fine for a book on the fourth day it is overdue?

A $0.60
B $0.70
C $0.80
D $0.90
E $1.00

A certain library assesses fines for overdue books as follows:

On the first day that a book is overdue, the total fine is $0.10.

For each additional day that the book is overdue the total fine is either increased by $0.30 or double, whichever results in the lesser amount.

What is the total fine for a book on the fourth day it is overdue?

A $0.60
B $0.70
C $0.80
D $0.90
E $1.00

Solution:

We need to determine the total amount of a fine for a book that is 4 days overdue. Let's determine each fine levied for when the book is overdue 1, 2, 3, or 4 days.

1 day overdue: $0.10

2 days overdue: The lesser of ($0.10 + $0.30 = $0.40) or (2 x $0.10 = $0.20)

Thus, the total fine for a book that is 2 days overdue is $0.20.

3 days overdue: The lesser of ($0.20 + $0.30 = $0.50) or (2 x $0.20 = $0.40)

Thus, the total fine for a book that is 3 days overdue is $0.40.

4 days overdue: The lesser of ($0.40 + $0.30 = $0.70) and (2 x $0.40 = $0.80)

Thus, the total fine for a book that is 4 days overdue is $0.70.

Note that the problem says the "total fine" is either increased by $0.30 or doubled. That is why, for each day's calculation, we didn't need to add the previous day's fine. If you don't read carefully, you might end up doubling the fine and adding it to the previous day's fine.

Answer: B