An auditorium has rows of seats with 8 seats in each row. Kayla knows there are at least 70 seats but fewer than 150 seats in the auditorium. How many rows of seats can there be in the auditorium?

1. Explain how you would find the least possible number of rows in the auditorium.
- Calculate: [tex]$\frac{70}{8} = 8.75$[/tex], which implies 9 rows (round up).

2. How would you find all the possible numbers of rows, without having to check if 8 is a factor of every number between 70 and 150?
- Find the smallest integer greater than or equal to [tex]$\frac{70}{8}$[/tex] and the largest integer less than [tex]$\frac{150}{8}$[/tex].

3. Name all the possible numbers of rows in the auditorium.
- Possible numbers of rows: 9 to 18 (inclusive).

To determine the possible numbers of rows in the auditorium, we need to know how many combinations of rows with 8 seats each can add up to a number between the minimum and maximum seat counts given. Here's a step-by-step explanation:

1. Understand the Problem:
- The auditorium has rows with 8 seats each.
- There are at least 70 seats and fewer than 150 seats.

2. Find the Least Possible Number of Rows:
- To find the minimum number of rows, divide the minimum seats (70) by the seats per row (8).
- [tex]$70 \div 8$[/tex] gives 8 with a remainder.
- Since you can't have a fraction of a row, round up to the nearest whole number, which is 9.
- So, the least number of rows is 9.

3. Find the Greatest Possible Number of Rows:
- For the maximum, divide the maximum seats available (which is one less than 150, so 149) by the seats per row (8).
- [tex]$149 \div 8$[/tex] gives 18 with some fraction leftover, so we take the whole number part.
- Hence, the greatest number of rows is 18.

4. Determine All Possible Numbers of Rows:
- The possible numbers of rows range from the least number of rows (9) to the greatest number of rows (18).
- Therefore, the possible numbers of rows are 9, 10, 11, 12, 13, 14, 15, 16, 17, and 18.

By following these steps, we find that the auditorium can have anywhere from 9 to 18 rows, inclusive.