# Kathy D sells handcrafted decorations at flea markets.  The cost to rent a booth at the flea market is \$150.  The variable cost (of the material to make each item) is \$20. She plans to sell each...

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Kathy D sells handcrafted decorations at flea markets.  The cost to rent a booth at the flea market is \$150.  The variable cost (of the material to make each item) is \$20. She plans to sell each decoration for \$50.  How many must Kathy sell to break even?

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If she is actually able to make the handicrafts for \$20 apiece and to sell them for \$50 apiece, Kathy D will need to sell only 5 of the handicrafts to break even.  This is, of course, only true if she makes the handicrafts when they are ordered.  If she makes a whole bunch of them and keeps them as inventory, the answer will be different and it will depend on how many she keeps in inventory.

In economics, there are said to be two kinds of costs facing a business.  These are fixed costs and variable costs.  Kathy has \$150 in fixed costs that do not change regardless of how many or how few of her handicrafts she sells.  She has variable costs of \$20 per handicraft.  We therefore have to figure the point where her fixed and variable costs are equal to her revenues.  To do so, we must do a little basic algebra.

First, we set up our equation.  If x is the number of handicrafts sold, the equation will be:

Fixed costs + 20x = 50x

Since fixed costs  are 150, we have

150 + 20x = 50x

We then subtract 20x from both sides and we get

150 = 30x

We then divide each side by 30 and get

5 = x

That means she must sell 5 handicrafts to break even.  Let us check to be sure this is right.  If she sells 5 handicrafts at \$50 each, she gets \$250 in revenue.  If she makes 5, she spends \$100 (\$20 each) in variable costs and \$150 in fixed costs (for the booth).  Thus, she has taken in \$250 and spent \$250 and has broken even.

Therefore, Kathy must sell 5 handicrafts to break even.