The Country Buffet restaurant has tables that seat 6 people and booths that can seat 4 people. The restaurant has 38 seating units for seating a total of 188 people. Write a system of equations and use it to find the number of tables and the number of booths that are at the restaurant?

Define your variables for this system.

There are 20 booths and (38 - 20), or 18, tables

Step-by-step explanation:

Represent the number of tables with t and the number of booths with b.

We need to find the values of t and b.

(6 people/table) (t) + (4 people/booth) b = 188 (units are "people")

t + b = 38 (units are "seating units")

Solving the second equation for t, we get 38 - b = t.

Substitute 38 - b for t in the first equation:

(6 people/table) (38 - b) + (4 people/booth) b = 188

Then solve for b: 6 (38) - 6b + 4b = 188, or:

228 - 2b = 188, or 2b = 228 - 188, or 2b = 40. Thus, b = 20 (booths)

There are 20 booths and (38 - 20), or 18, tables.