Anew restaurant is to contain two-seat tables and four-seat tables. fire codes limit the restaurant's maximum occupancy to 72 customers. if the owners have hired enough servers to handle 22 tables of customers, how many of each kind of table should they purchase?

Let t and f be the number to two and four seat tables respectively.

t+f=22, solve for t

t=22-f, then we are told that capacity must be less than or equal to 72 people.

2t+4f≤72, using t found above in this equation we get:

2(22-f)+4f≤72 perform indicated multiplication on left side

44-2f+4f≤72  combine like terms on left side

44+2f≤72  subtract 44 from both sides

2f≤28  divide both sides by 2

f≤14  Since f=integer

f=14, and since t=22-f

t=8

So they should purchase 14 four seat tables and 8 two seat tables.