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.
