The owner of a new restaurant is designing the floor plan, and he is deciding between two different seating arrangements. The first plan consists of 24 tables a

Question

The owner of a new restaurant is designing the floor plan, and he is deciding between two different seating arrangements. The first plan consists of 24 tables and 11 booths, which will seat a total of 254 people. The second plan consists of 12 tables and 17 booths, which will seat a total of 242 people. How many people can be seated at each type of table?

Answer 1

Let x = the number of people that can be seated at a table

Let y = the number of people that can be seated in a booth

24x + 11y = 254

12x + 17y = 242    Multiply this equation by -2 and add it to the above equation.

-24x - 34y = -484

 24x + 11y = 254

         -23y = -230

               y = 10 per booth

24x + 11(10) = 254

24x + 110 = 254

24x = 144

x = 6 per table