Final answer:
The algebraic expression to calculate the number of people who can be seated when multiple rectangular tables are placed together end-to-end is s = 6 + 4(t - 1), where t is the number of tables. By applying this formula with t = 7, we find that 30 people can be seated.
Step-by-step explanation:
To determine how many people can be seated when 7 tables are placed together, we can create an algebraic expression based on the given information that 2 tables seat 10 people and 3 tables seat 14 people. Let's define t as the number of tables. From the information given, we can determine there is a base number of seats that one table provides when no other table is added, and for each additional table, there is a certain number of extra seats provided.
First, let's find out the seating pattern. With 2 tables, there are 10 seats, but when another table is added (making it 3 tables), there are 14 seats. Hence, each additional table after the first adds 4 more seats (14 - 10 = 4).
Given that one table alone does not provide 10 or 14 seats but a certain base number, we can denote this base number of seats as b. Therefore, we can represent the total number of seats (s) as a function of the number of tables (t) by the equation s = b + 4(t - 1).
To find the base number of seats from one table (b), we use the scenario with 2 tables: 10 = b + 4(2 - 1), which comes to 10 = b + 4. Solving for b we get b = 6. Therefore, the final algebraic expression to calculate the number of seats for any number of tables is s = 6 + 4(t - 1).
Using this expression, you can substitute 7 for t to find out how many people can be seated when 7 tables are placed together: s = 6 + 4(7 - 1). This simplifies to s = 6 + 4(6) or s = 6 + 24, giving us a total of 30 seats for 7 tables.