The Bookworm had 20 copies of Raising Your Rabbit Right!. After a week they had 17 copies left. At the end of two weeks they had 16 copies left and after three weeks they had 13 copies left. At the end of four weeks they had 12 copies left. If they kept selling copies of the book at this same rate, how many copies would they have left at the end of nine weeks?
copies sold per week = (20-12)/4 = 2 copies / week sold
2*9 = 18
20 - 18 = 2
Alternate -3 and -1. At 5 weeks, 9 left, at 6 weeks, 8 left, at 7 weeks, 5 left...and so on.
To solve this problem, we'll track the pattern and find the decreasing rate of book sales.
In the first week, The Bookworm had 20 copies, and after that week, they had 17 copies left. So, they sold 20 - 17 = 3 copies in the first week.
In the second week, they had 17 copies, and after that week, they had 16 copies left. So, they sold 17 - 16 = 1 copy in the second week.
In the third week, they had 16 copies, and after that week, they had 13 copies left. So, they sold 16 - 13 = 3 copies in the third week.
In the fourth week, they had 13 copies, and after that week, they had 12 copies left. So, they sold 13 - 12 = 1 copy in the fourth week.
We can observe that the pattern of book sales is 3, 1, 3, 1, and it repeats.
To find out how many copies they would have at the end of nine weeks, we need to calculate the number of copies sold in the five-week cycle.
Total copies sold in the five-week cycle = 3 + 1 + 3 + 1 = 8
Now, let's divide the number of weeks (nine) by the length of the cycle (five) to find out how many cycles are completed:
Number of cycles = 9 ÷ 5 = 1 cycle with a remainder of 4 weeks
Since we know that one cycle consists of selling 8 copies, we multiply the number of cycles (1) by the number of copies sold in a cycle (8):
Number of copies sold in completed cycles = 1 cycle x 8 copies = 8 copies
In the remaining 4 weeks, we can use the pattern of sales from our first four weeks (3, 1, 3, 1).
The first week of the remaining 4 weeks would be a 3 (copies sold), the second week a 1, the third week a 3, and the fourth week a 1.
Adding these additional sales to the copies sold in completed cycles:
Total copies sold in all weeks = 8 + 3 + 1 + 3 + 1 = 16 copies sold
To calculate the number of copies they would have left at the end of nine weeks, subtract the total copies sold from the initial number of copies:
Number of copies left at the end of nine weeks = Initial number of copies - Total copies sold
= 20 copies - 16 copies
Therefore, The Bookworm would have 4 copies left at the end of nine weeks.