A restaurant has a total of 50 tables. Some of the tables can seat 6 people and some can sit 2 people. All of the seats are occupied when there 172 people seated. How many tables for 6 are there?

Answer 1

Let x = #6-seat tables

Let y = #2-seat tables

x + y = 50 [there are 50 tables in total]

6x + 2y = 172 [6 people at x tables + 2 people at y tables total 172 people]

y = 50 - x [solve first equation for y]

6x + 2(50 - x) = 172 {substitute 50 - x for y in 2nd equation]

6x - 2x = 172 - 100

4x = 72

x = 18

y = 50 - 18 = 32

So there are 18 tables holding 6 people and 32 tables holding 2 people.

Check:

18(6) = 108

32(2) = 64

108 + 64 = 172