Question

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.The members of a cooking club are making cakes, which they will sell at a street fair for $18 apiece. It cost $17 for a booth at the fair, and the ingredients for each cake cost $1. At some point, the club members will sell enough cakes so that their sales cover their expenditures. How many cakes will they have sold? How much will the sales and expenditures be?

Answer 1

Let:

C = Total cost

R = Total revenue

x = Number of cakes

a = Cost of the ingredients for each cake = $1

b = Cost of a booth at the fair = $17

c = Selling price of each cake = $18

Therefore:

$\begin{gathered} C=ax+b \\ C=x+17 \\ ------- \\ R=18x \end{gathered}$

At some point, the club members will sell enough cakes so that their sales cover their expenditures. Therefore:

$\begin{gathered} C=R \\ x+17=18x \\ _{\text{ }}solve_{\text{ }}for_{\text{ }}x\colon \\ 18x-x=17 \\ 17x=17 \\ x=\frac{17}{17} \\ x=1 \end{gathered}$

Answer:

1 cake and $18