Question

Combinatorics is a branch of math focused on arrangements of

objects. Jorge is an event organizer who must seat 102 guests.
He has circular tables that seat 10 people each and square tables
that seat 4 people each. He wants to use as many circular tables
as possible but have no empty seats. Explain how he could
arrange the tables he will need.
Activity

Answer 1

He needs 9 circular tables and 3 square tables.

Explanation:

Given:

Number of persons in each circular table = 10

Number of persons in each square table = 4

Now, in order to maximize number of circular tables, we must find the maximum multiple of 10.

Multiples of 10 = 10, 20, 30, 40, 50, 60, 70, 80, 90, 100.

Now, if we take 100, then the seats remaining are 2. But the square tables require 4 persons. So, 100 is not correct.

Next, if we choose 90 as a multiple of 10, then the circular tables used would be
`(90)/(10)=9`.

Now, number of guests left are 102 - 90 = 12. Now, 12 is a multiple of 4. So, 3 square tables can accommodate 12 persons as
`4* 3=12`.

Therefore, he has to use 9 circular tables and 3 square tables to maximize the number of circular tables.