Final answer:
To seat 12 people with the given table arrangement in a cafeteria, 5 tables are required.
Step-by-step explanation:
The question involves determining the number of cafeteria tables needed to seat 12 people when two people can sit at the long side of each table and one person can sit at the short side. To figure this out, we need to calculate the total number of people that can be seated per arrangement of tables.
For one table, we can seat 4 people (2 on each long side). When two tables are pushed together, we eliminate two seats (since the short sides of the tables are now unavailable), resulting in seating for 6 people (2 on the long side of each table, plus one at the remaining short sides). With each additional table, we add only 2 more seats.
Thus, the pattern is as follows: 1 table seats 4, 2 tables seat 6, 3 tables seat 8, 4 tables seat 10, and 5 tables seat 12. Therefore, to seat 12 people, we will need 5 tables.