Question

A new restaurant is to contain six-seat booths and five-seat round tables. Fire codes limit the restaurants maximum occupancy to 97 customers. If the owners have hired enough servers to handle 17 tables of customers, how many of each kind of table should they purchase?

Answer 1

x = number of 5-seat tables

y = number of 6-seat booths

Its given that fire code limits are given in terms of "customers," not people.

Also its given that fire codes limit the restaurants maximum occupancy to 97 customers.

5x+6y=97.....(1)

Its given that owners has hired enough servers to handle 17 tables of customers.

x+y=17.......(2)

x=17-y........(3)

substituting equation(3) in (1) we get

5*(17-y)+6y=97

85-5y+6y=97

y=97-85

y=12

x=17-y

x=17-12

x=5

x = number of 5-seat tables=5

y = number of 6-seat booths=12