Question

When designing a new school cafeteria, the school administrators planned for there to be twice as many tables in each row as there are rows. After increasing the size of the cafeteria, it was decided to add 3 more rows of tables and to increase the original number of tables in each row by 2. The maximum number of tables the cafeteria can hold is 126.

If r represents the original number of rows the school administrators planned to have in the cafeteria, which of the following represents this situation?

A.
2r2 + 7r + 6 ≤ 126
B.
2r2 + 8r + 6 ≥ 126
C.
2r2 + 7r + 6 ≥ 126
D.
2r2 + 8r + 6 ≤ 126

Answer 1

D.

Explanation:

i belive it will be that baded on the fact it said twice as many rows.

Answer 2

The original cafeteria plan, considering twice as many tables in each row as there are rows, is correctly represented by the inequality 2r^2 + 8r + 6 ≤ 126.

Let's denote the original number of tables in each row as "t" and the original number of rows as "r". The total number of tables in the original cafeteria is then t * r.

According to the given information, the school administrators planned for there to be twice as many tables in each row as there are rows. So, t = 2r.

The total number of tables in the cafeteria, before any changes, is t * r = 2r^2.

After increasing the size of the cafeteria, 3 more rows of tables were added, and the original number of tables in each row was increased by 2. Therefore, the new total number of tables is (t + 2) * (r + 3).

This can be expressed as (2r + 2) * (r + 3) since t = 2r. Expanding and simplifying:

2r^2 + 6r + 2r + 6

2r^2 + 8r + 6

Now, we set up the inequality based on the maximum number of tables the cafeteria can hold:

2r^2 + 8r + 6 ≤ 126

Therefore, the correct representation of the situation is option:

2r^2 + 8r + 6 ≤ 126