Question

A room contains 36 chairs arranged in rows. The number of rows is one more than twice the number of chairs per row. Find the number of rows.

Answer 1

The question asks to find the number of rows when 36 chairs are arranged in a room, with the rows being one more than twice the number of chairs per row. The solution involves setting up and solving a quadratic equation, which leads to the finding that there are 4 chairs per row and therefore 9 rows in total.

Step-by-step explanation:

The student is asking how to determine the number of rows in a room given the number of chairs and a relationship between the number of rows and chairs per row. To solve this, let's denote the number of chairs per row as x. According to the problem, the number of rows is one more than twice the number of chairs per row, which can be expressed as 2x + 1. We also know that the total number of chairs is 36, so the equation to solve is x(2x + 1) = 36.

Step-by-Step Solution:

1. Write down the equation based on the given information: x(2x + 1) = 36.
2. Multiply out the left side of the equation to get 2x2 + x - 36 = 0.
3. Factor the quadratic equation to find the values of x.
4. Solving the quadratic equation will give us two possible values for x, but only the positive value makes sense in the context of this problem.
5. Find the number of rows by substituting the value of x into 2x + 1.

Upon solving, we discover that the number of chairs per row is 4 and the number of rows is 9.

Answer 2

26 chairs because it tells you there one more then twice