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Yolanda arranges small square tables in a straight line. One person sits on each side of a table. How many people can sit at 4 tables?

Mathematics

ScanSolve AI Answer

Answer

P=2N+2P = 2N + 2

Step-by-step solution

3 steps

Activity 2: Table Arrangement Pattern

The image describes how Yolanda arranges small square tables in a straight line, with one person sitting on each side of the table.

  1. Observe the pattern for the number of people.

    • For 1 table: There are 2 people on the long sides and 2 people on the ends. Total = 2+2=42 + 2 = 4 people.
    • For 2 tables: There are 2 people on the long sides of each table (2×2=42 \times 2 = 4) and 2 people on the ends. Total = 4+2=64 + 2 = 6 people.
    • For 3 tables: There are 2 people on the long sides of each table (3×2=63 \times 2 = 6) and 2 people on the ends. Total = 6+2=86 + 2 = 8 people.
    • For 4 tables (as shown in the diagram): There are 2 people on the long sides of each table (4×2=84 \times 2 = 8) and 2 people on the ends. Total = 8+2=108 + 2 = 10 people.
  2. Identify the rule for the pattern.

    From the observations, for every additional table, 2 more people can be seated. This suggests a relationship involving multiplication by 2. The 2 people at the ends of the arrangement remain constant regardless of the number of tables.

    Let NN be the number of tables and PP be the number of people.
    The number of people can be calculated as:

    P=(2×N)+2P = (2 \times N) + 2
  3. Verify the rule with the given example.

    For N=4N = 4 tables:

    P=(2×4)+2P = (2 \times 4) + 2 P=8+2P = 8 + 2 P=10P = 10

    This matches the example given in the problem statement.

    The rule for the number of people (PP) who can sit at NN tables is:

    P=2N+2\boxed{P = 2N + 2}

    The specific questions for Activity 2 are not visible in the image, but this rule describes the pattern.

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