Use the image to answer the question.

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.

(1 point)
tables
Remaining Attempts : 3

Answer 1

To determine how many tables would be needed for 16 people using the pattern given in the illustration:

1. Identify the pattern:

   • 1 table seats 4 people: 1 table for 4 people
   • 2 tables seat 6 people: 2 tables for 6 people
   • 3 tables seat 8 people: 3 tables for 8 people

2. Define the sequence: From the data we see a noticeable pattern:

   • For each increase in the number of tables, the seating increases by 2 people per additional table.
   • Specifically:
     • 1 table seats 4 people,
     • 2 tables (4 + 2) = 6 people,
     • 3 tables (6 + 2) = 8 people,
     • so for n tables, the number of people seated is given by the formula: \[ \text{People seated} = 4 + 2(n - 1) \]

3. Finding the number of tables for 16 people:

   • We set up the equation knowing we need to find n such that: \[ 4 + 2(n - 1) = 16 \]
   • Simplifying the equation: \[ 4 + 2n - 2 = 16 \] \[ 2n + 2 = 16 \] \[ 2n = 14 \] \[ n = 7 \]

So, 7 tables would be needed for 16 people.