SOLUTION: A restaurant has tables for 4 and six. There is a total tables of 32, with seats for 152 patrons. How many tables for six are there?

We can do the problem with or without algebra.  We'll do it both ways.

Without algebra:
Tables for 4 are tables for 2 couples and tables for 6 are tables for 3 couples.
There are seats for 152 patrons, or for 152÷2 or 76 couples. If all 32 tables
were tables for 2 couples there would only be seats for 32×2 or 64 couples.
So the other seats for the 76-64 or 12 couples must be at tables for 3 couples.
So there are 12 tables for 6 (and 32-12 or 20 tables for 4).

Answer: 12 tables for six.

With algebra.

Make this chart:

            number       seats      number or
           of tables   per table      seats      
---------------------------------------------
for four    32-x          4          4(32-x)
for six       x           6            6x
---------------------------------------------
totals        32                      152

The equation comes from:




    

Solve that and get x=12, or 12 tables for six, (and 32-12=20 tables for four). 

Edwin