Question

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.

Answer 1

t + b = 38

Explanation:

k12 the other guy had the right idea jus didn't simplify

Answer 2

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

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.