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?

Rationale

There will be 22 rows of chairs.

To find the number of rows, we can set up an equation based on the problem's description. Let the number of rows be represented by \( r \). Then the number of chairs in each row will be \( r + 8 \). The total number of chairs is given by the equation \( r \times (r + 8) = 660 \). Solving this quadratic equation yields \( r = 22 \).

A (12) YOUR ANSWER

If there are 12 rows, then the number of chairs per row would be \( 12 + 8 = 20 \), leading to a total of \( 12 \times 20 = 240 \) chairs. This total is significantly less than 660, making this option incorrect.

B (22) CORRECT

With 22 rows, the number of chairs in each row would be \( 22 + 8 = 30 \). Multiplying gives a total of \( 22 \times 30 = 660 \) chairs, which matches the requirement perfectly, confirming this choice as correct.

C (26) YOUR ANSWER

For 26 rows, the number of chairs per row would be \( 26 + 8 = 34 \). The total would be \( 26 \times 34 = 884 \) chairs, which exceeds 660, thus making this option invalid.

D (30) YOUR ANSWER

If there are 30 rows, then the chairs per row would be \( 30 + 8 = 38 \), resulting in \( 30 \times 38 = 1140 \) chairs. This is also much greater than 660, ruling this option out.

E (55) YOUR ANSWER

With 55 rows, the chairs per row become \( 55 + 8 = 63 \). The total would then be \( 55 \times 63 = 3465 \) chairs, which is far too high compared to 660, making this choice incorrect.

Conclusion

Through the setup of a quadratic equation based on the relationship between rows and chairs, we determined that 22 rows lead to the correct arrangement of 660 chairs. Other options either result in totals that are too low or too high, affirming the uniqueness of the solution found.

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?

There will be 22 rows of chairs.

Related Questions

Related Quizzes

How familiar were you with this question?

Report an Issue

Rate this Practice Test