The library at Miller Elementary School has an odd number of tables. Some tables will seat 4 students and some tables that will seat 6 students. A total of 32 students can sit at the tables with no empty seats. What is the number of tables of each type?

Answer 1

f = # of 4-student tables
s = # six-student tables

total students:
4f + 6s = 32
or,
2f + 3s = 16

Now, 2f is even, so 3f must be even to add to 32, an even number. So, s must be even.

possible solutions:
(f,s) = (2,4),(5,2)

since there are an odd number of tables,
5 seat 4 students, 2 seat six students.