Inequalities

Question

Hassan stores books in large boxes and small boxes . Each large box holds 20 books and each small box holds 10 books. He has x larg boxes and y small boxes
Hassan must store at least 200 books. Show that 2x+y>20

Answer 1

You know, sometimes problems just aren't presented well. Remember they're presenting a relationship about the number of boxes needed, but what's up with this "20"? Where did it come from?! What I like to do is create my own problem from the data:

If I want to store at least 200 books, I know that  20 bks/lg·x lg + 10 bks/sm ·y sm > 200  (It should be ≥ in my opinion since the problem says "at least", but you can only argue so much.) Hmmm, look what happens if we simplify.

20x + 10y > 200; factor 10 from both terms on the left

10(2x+y) > 200; divide both sides by 10

2x+y > 20  PROVEN! You're awesome!

Is this useful? Sure. Let's say you have 5 large boxes left. You'll need y>20-2(5) or at least 10 small boxes. 5lg(20bk/lg)+10sm(10bks/sm) = 100 bks + 100 bks = 200 bks. So you can check your inventory and see if you've got enough small boxes to get these suckers put away!