Rationale
There will be 22 rows of chairs.
To solve this problem, we set up the equation based on the relationship between the number of rows (r) and the number of chairs in each row (r + 8). The total number of chairs is 660, leading to the equation r(r + 8) = 660, which simplifies to r^2 + 8r - 660 = 0. Solving this quadratic equation yields r = 22 as the valid solution.
A) If there are 12 rows, then the number of chairs in each row would be 12 + 8 = 20. Multiplying these gives a total of 12 * 20 = 240 chairs, which is far less than 660. Thus, this choice does not satisfy the total number of chairs required.
B) With 22 rows, the number of chairs per row would be 22 + 8 = 30. This results in a total of 22 * 30 = 660 chairs, which exactly matches the requirement. Therefore, this is the correct answer.
C) If there are 26 rows, then the number of chairs in each row would be 26 + 8 = 34. This results in a total of 26 * 34 = 884 chairs, which exceeds 660. Hence, this option is incorrect.
D) Assuming there are 30 rows, the number of chairs per row would be 30 + 8 = 38. The total would then be 30 * 38 = 1140 chairs, which is much greater than 660. Therefore, this choice does not work.
E) With 55 rows, the number of chairs in each row would be 55 + 8 = 63. This results in a total of 55 * 63 = 3465 chairs, which is significantly higher than 660. Thus, this option is also incorrect.
Conclusion
In this problem, we determined the number of rows of chairs by establishing the relationship between rows and chairs per row. The only option that satisfies the condition of having a total of 660 chairs is B) 22 rows, confirming the proper arrangement of chairs in the gymnasium. Other options do not yield the correct total and therefore are invalid.