Question

In the cafeteria, there is one large table with 10 seats and many smaller tables with 4 seats. The cafeteria has a fire code restriction that the room can hold a maximum of 70 students. If a student is seated at every seat at each table, how many small tables can be in the cafeteria without breaking the fire code?
Write an inequality to represent the situation. Use x to represent the number of small tables.

Answer 1

To represent the situation with an inequality, we can set up the equation based on the seating arrangements described.

1. The large table has 10 seats.
2. Each small table has 4 seats.
3. The maximum number of students that can be seated in the cafeteria is 70.

Let \( x \) represent the number of small tables. Since each small table has 4 seats, the total number of seats provided by the small tables would be \( 4x \).

We can write an inequality that includes the seats at the large table plus the seats provided by the small tables, and sets that sum less than or equal to 70:

\[
10 + 4x \leq 70
\]

This inequality represents the total number of students that can be seated in the cafeteria without exceeding the fire code restriction. To solve for \( x \), you can subtract 10 from both sides:

\[
4x \leq 60
\]

Now, divide both sides by 4:

\[
x \leq 15
\]

This means that there can be at most 15 small tables in the cafeteria without breaking the fire code.