Question

A new 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?

Answer 1

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.