#1**+1 **

x = number of round tables and y = number of rectangular tables

Each round table has 6 chairs. Each rectangular table has 10 chairs.

The total number of chairs must be greater than or equal to 185 .

6x + 10y ≥ 185

There must be no more than 15 rectangular tables.

So the number of rectangular tables must be less than or equal to 15 .

y ≤ 15

There must be no fewer than 6 round tables.

So the number of round tables must be greater than or equal to 6 .

x ≥ 6

The number of rectangular tables must be greater than or equal to one-third the number of round tables.

y ≥ \(\frac13\)x

3y ≥ x

x ≤ 3y

hectictar
Mar 4, 2018