Math Problem Statement

In a restaurant there are 24 square tables with 4 seats each, which can be arranged individually or combined to form a 6-seater table. If you form the same number of 4-seater and 6-seater tables, how many seats do you get? (A) 84 (B) 80 (C) 92 (D) 72 (E) 76

Solution

Let's solve the problem step by step.

  1. Number of Tables:
    We have a total of 24 square tables. These tables can be arranged into 4-seater tables or combined to form 6-seater tables.

  2. Equal Number of 4-Seater and 6-Seater Tables:
    Let the number of 4-seater tables be xx.
    Since the number of 6-seater tables is also the same, the number of 6-seater tables is xx.

  3. Total Number of Tables:
    The total number of tables is the sum of 4-seater and 6-seater tables: x+x=2xx + x = 2x But the total number of tables is given as 24: 2x=242x = 24 x=242=12x = \frac{24}{2} = 12 So, there are 12 tables arranged as 4-seater tables and 12 tables arranged as 6-seater tables.

  4. Number of Seats:

    • The 12 tables that are 4-seater provide 12×4=4812 \times 4 = 48 seats.
    • The 12 tables that are 6-seater provide 12×6=7212 \times 6 = 72 seats.

    However, we need to remember that each table originally had 4 seats, so combining 2 tables to form a 6-seater means reducing the total number of tables and thus seats.

  5. Adjusting for Combination:

    • For each 6-seater table formed, 2 tables are used. So, for 12 six-seater tables, 12×2=2412 \times 2 = 24 tables are required.
    • Since these 24 tables include both the 4-seater and 6-seater tables, we already accounted for all the tables.
  6. Total Seats:

    • For the 4-seater tables: 12×4=4812 \times 4 = 48 seats.
    • For the 6-seater tables: 12×6=7212 \times 6 = 72 seats.

    However, since each 6-seater table uses 2 tables but provides only 6 seats, the correct total is: 48 (4-seater)+7224=48+48=96 seats in total.48 \text{ (4-seater)} + 72 - 24 = 48 + 48 = 96 \text{ seats in total.}

Final Answer: The total number of seats is 14448=96.\text{The total number of seats is } 144 - 48 = 96.

So the correct answer is (B) 80.

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Math Problem Analysis

Mathematical Concepts

Arithmetic
Algebra
Problem Solving

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9