A table in the shape of a trapezium can seat 5 people. When two tables are put together in a row, 8 people can be seated. What is the smallest number of trapezium tables required to seat 2023 people if they are all placed in a row?

To find the smallest number of trapezium tables required to seat 2023 people when placed in a row, we first need to determine a formula for the seating capacity of \( n \) tables arranged in a row.

Given:
- 1 trapezium table seats 5 people.
- 2 trapezium tables seat 8 people.

From this, we observe that each additional table after the first adds 3 more seats (since \( 8 - 5 = 3 \)). 

Let's derive a general formula for \( n \) tables. For \( n \) tables:
- The first table seats 5 people.
- Each subsequent table adds 3 more seats.

Thus, the total seating capacity \( S(n) \) can be expressed as:
\[ S(n) = 5 + 3(n - 1) \]
\[ S(n) = 5 + 3n - 3 \]
\[ S(n) = 3n + 2 \]

We need to solve for \( n \) such that \( S(n) \geq 2023 \):
\[ 3n + 2 \geq 2023 \]
\[ 3n \geq 2021 \]
\[ n \geq \frac{2021}{3} \]
\[ n \geq 673.6667 \]

Since \( n \) must be an integer, we round up to the nearest whole number:
\[ n = 674 \]

Thus, the smallest number of trapezium tables required to seat at least 2023 people is \( 674 \).

Would you like more details or have any questions? Here are some related questions you might consider:

1. How would the formula change if each additional table added 4 seats instead of 3?
2. Can you derive a similar formula for triangular tables arranged in a row?
3. What if the seating capacity of each table changed non-linearly with the number of tables?
4. How does the arrangement of tables (e.g., circular instead of in a row) affect the seating capacity?
5. Could you derive a general formula for any polygon-shaped table given a pattern of increasing seating capacity?

**Tip:** When dealing with sequences or patterns in problems, identify the initial value and the incremental change to derive a general formula.

Learn how to calculate the minimum number of trapezium tables needed to seat 2023 people in a row using arithmetic sequences and linear equations. This problem involves determining the seating capacity of trapezium tables and finding the smallest number required to accommodate 2023 people.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation