Ava is starting a cake-baking business and has spent $150 on equipment. Each cake costs $4.50 to make, and she plans to sell them for $12 each. Ava wants to find the number of cakes, $ c $, she must sell to break even. In other words, she wants to know how many cakes she must sell before she has made as much money as she has spent.

Which equation can she use?

A. $ 150 + 4.5c = 12c $

B. $ 150 - 4.5c = 12c $

C. $ c(150 + 4.5) = 12c $

D. $ 4.5c + 12c = 150 $

E. $ 4.5c + 150 = 12 $

F. $ 150c + 4.5 = 12 $

How many cakes must Ava sell before she has made as much money as she has spent?

____ cakes

The breakeven quantity is the number of cakes that Ava needs to make in order to cover all costs incurred in producing cakes, in essence, it is the number cakes that makes total revenue to be the same as the total costs, which can be modeled using the below breakeven unit formula:

total revenue=total costs

total revenue=selling price*breakeven units

selling price=12

breakeven units=c

total revenue=12c

total costs=fixed costs+(variable cost*breakeven units)

fixed costs=cost of equipment=150

variable cost per cake=4.5

total costs=150+4.5c

12c=150+4.5c

150+4.5c=12c

150=12c-4.5c

150=7.5c

c=150/7.5

c=20

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