They need to sell 5 pieces to cover their expenditures (have a profit of zero).
How many cakes will they have sold?
We know that the costs are:
- $30 for the booth at the fair.
- $2 for each piece of cake they sell.
And the revenue is:
- $8 for each piece of cake.
So, the profit (the difference between the revenue and the cost) for selling x pieces is:
p(x) = $8*x - $2*x - $30
p(x) = $6*x - $30
We want to find the value of x such that p(x) = 0, then:
0 = $6*x - $30
x = $30/$6 = 5
They need to sell 5 pieces to cover their expenditures (have a profit of zero).
If you want to learn more about profit:
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