Answer :
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.
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.