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Question

An illustration shows a square with four stars along the edges, two squares attached with six stars along the outer edges; and three squares attached with eight stars along the outer edges.

The tables for a party are seated as 4 people at 1 table, 6 people at 2 tables, and 8 people at 3 tables. Use a sequence to determine how many tables would be needed for 16 people.

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Answer 1

To determine how many tables would be needed for 16 people using the sequences given:

1. 1 table seats 4 people.
2. 2 tables seat 6 people.
3. 3 tables seat 8 people.

From the examples, we can see the pattern:

• 4 people require 1 table.
• 6 people require 2 tables, which indicates that each additional table (above the first) accommodates 2 additional people.
• 8 people require 3 tables, indicating that adding another table accommodates 2 additional people.

This shows us:

• The first table accommodates 4 people.
• Each subsequent table accommodates an additional 2 people.

To find out how many tables are needed for 16 people:

• The first table accommodates 4 people, leaving us to seat 12 more people.
• Each additional table (after the first) can seat 2 more people.
• The equation can be set as follows:

Total people - People at the first table = Remaining people to seat

Remaining people to seat = 16 - 4 = 12

Calculating how many additional tables we need:

• Each additional table seats 2 people.
• Thus, 12 people would require 12/2 = 6 additional tables.

Now, adding the first table:

• 1 (for the first table) + 6 (additional tables) = 7 tables in total.

Therefore, the answer is 7 tables.