Question

An event has 8 adults and 12 children. The event planner wants to make each table identical, with the same combination of adults and children and no people left over. What is the greatest number of tables the planner can set up?

Answer 1

Explanation:

To make each table identical, we need to find the greatest common divisor (GCD) of 8 and 12, which will give us the maximum number of people that can be seated at each table.

We can find the GCD using the Euclidean algorithm:

12 = 8 × 1 + 4

8 = 4 × 2 + 0

Since the remainder is 0, the GCD of 8 and 12 is 4.

Therefore, the event planner can set up tables with 4 people at each table (2 adults and 2 children).

There are a total of 20 people (8 adults + 12 children), so the number of tables needed is:

20 ÷ 4 = 5

Thus, the greatest number of tables the planner can set up is 5.