To determine the number of tables needed for 16 people given the seating arrangements provided, we can first summarize the information:
- 1 table can seat 4 people.
- 2 tables can seat 6 people (which implies each table seats 3 people when spread across two tables).
- 3 tables can seat 8 people (which implies each table seats approximately 2.67 people).
Next, we can recognize a pattern to the number of people per table:
- 1 table seats 4 people
- 2 tables seat 6 people: Each table now has 3 people, which is less than 4.
- 3 tables seat 8 people: Each table now can seat approximately 2.67 people, which is again less.
It appears that as we increase the number of tables, the average number of people seated per table decreases.
Let’s arrange the seating data in a more systematic sequence. We can observe:
- For 1 table: 4 people → 1 table
- For 2 tables: 6 people → this is not consistent with the previous table.
- For 3 tables: 8 people → each table is approximately (8/3 ≈ 2.67) people.
To find a functional approach to determine how many tables would be needed for 16 people, we will continue the examination by extrapolating from the current data.
We notice that:
- Going beyond one table is resulting in lower seating capacity per table; thus as we add more tables, we need to find the pattern for larger numbers.
Let's extrapolate:
- At 1 table, we fit 4 people.
- Adding a second table meant we could seat about 6 people total, or roughly 3 each.
- Then by the third table, we could seat 8 people total.
After these observations, let's consider how many people we can seat at increasing number of tables:
- If we assumed a somewhat even decrease in seating, it would appear that initially, we start spacious (4, 3) but that drops as we add more tables.
If we were to follow the trend, to find out how many tables fit 16 people, we see:
- For 4-5 tables, we'd maximize better distribution towards 2 or 3 per table.
Rounding this logic: Assuming we continue practicing a diminishing return, estimating further down we could assume:
- For 4 tables estimated seating could be at least 10-12 comfortably yet adjusting ratios lower each visit.
Thus after trying several estimates: After observations and mathematical modeling of diminishing returns between table counts and persons, it’d be reasonable to estimate that about 8 tables might need to be used, assuming around 2-3 people to ensure effective seating for the total of 16.
Therefore, the number of tables needed for 16 people is around 8 tables, on average estimation.
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