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

## Inequalities

# 1 Answer

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!