To determine how many tables are needed for 16 people based on the seating arrangements provided, we can analyze the current seating configurations:
- At 1 table: 4 people
- At 2 tables: 6 people
- At 3 tables: 8 people
From the description, it seems that the number of people seated increases by 2 for every additional table:
- 1 table (4 people)
- 2 tables (6 people) → increase of 2 people over 1 table
- 3 tables (8 people) → another increase of 2 people over 2 tables
From this, we can conclude that each table seats 2 additional people.
Now, we can represent this as a function of the number of tables \( t \):
- People seated \( P(t) = 2t + 2 \)
Using this function:
- For 1 table: \( P(1) = 2(1) + 2 = 4 \)
- For 2 tables: \( P(2) = 2(2) + 2 = 6 \)
- For 3 tables: \( P(3) = 2(3) + 2 = 8 \)
Now we need to find out how many tables are needed for 16 people: \[ P(t) = 16 \] \[ 2t + 2 = 16 \] Subtracting 2 from both sides: \[ 2t = 14 \] Dividing by 2: \[ t = 7 \]
Thus, we would need 7 tables to seat 16 people.
Answer: 7 tables