MPM 2D- Chapter 1 Linear Systems
Word Problems
Break Even Point
Modeling Linear Equations
Sometimes,
the y = mx + b types of problems involve “break even points” (the POI)
The break even point in business represents the exact moment when
money spent = money earned (zero profit)
(or how many things do I have to sell to cover off my spending costs)
the y represents Money Earned or Money Spent
the x represents the number of things sold or bought
One equation represents:
money spent = initial amount of money spent (b) plus a per item cost (mx)
The other equation represents:
money earned =per item selling price (mx) (what happened to the “b”? It’s zero!)
Let’s try to model the following break even situation:
You are starting a business that sells designer doggie sunglasses. Your startup costs for the
business are $4800 (buy a computer, design a website, conduct research, get a celebrity canine
to endorse your product). It also costs $40 to manufacture each pair of glasses.
If you sell the sunglasses for $100 each, how many must you sell to break even?