8. Chairs are to be arranged in a school gymnasium so that the number of chairs in each row will be 8 greater than the number of rows. If a total of 660 chairs are to be arranged in this fashion, how many rows of chairs will there be?
Answer: B
There will be 22 rows of chairs.
The arrangement of chairs in the gymnasium results in a scenario where the number of chairs in each row is 8 greater than the number of rows. Given that there are a total of 660 chairs, this leads us to determine that the number of rows is 22.
A) 12
Choosing 12 as the number of rows leads to a calculation of chairs per row as 12 + 8 = 20. Consequently, the total number of chairs would be 12 rows × 20 chairs/row = 240 chairs. This total does not meet the requirement of 660 chairs, making this option incorrect.
B) 22
With 22 rows, the calculation shows that the number of chairs per row is 22 + 8 = 30. Thus, the total number of chairs would be 22 rows × 30 chairs/row = 660 chairs. This matches the total chairs available, confirming that this option is correct.
C) 26
If there are 26 rows, the number of chairs in each row would be 26 + 8 = 34. Therefore, the total number of chairs would be 26 rows × 34 chairs/row = 884 chairs. This exceeds the total of 660 chairs, indicating that this option is incorrect.
D) 30
Selecting 30 rows results in each row having 30 + 8 = 38 chairs. The total number of chairs would then be 30 rows × 38 chairs/row = 1140 chairs. This is also greater than the total of 660 chairs, making this option incorrect.
E) 55
Choosing 55 rows leads to 55 + 8 = 63 chairs per row. The calculated total would be 55 rows × 63 chairs/row = 3465 chairs, which is significantly more than 660 chairs. Hence, this option is incorrect.
Conclusion
Option B, with 22 rows, is definitively correct as it produces the exact total of 660 chairs needed. All other options fail to meet this requirement either by falling short or exceeding the total number of chairs to be arranged. Thus, B is the only viable solution in this context.