The members of a cooking club are making cakes, which they will sell at a street fair for $16 apiece. It cost $52 for a booth at the fair, and the ingredients for each cake cost $3. At some point, the club members will sell enough cakes so that their sales cover their expenditures. How much will the sales and expenditures be? How many cakes will they have sold?

Question

The members of a cooking club are making cakes, which they will sell at a street fair for $16 apiece. It cost $52 for a booth at the fair, and the ingredients for each cake cost $3. At some point, the club members will sell enough cakes so that their sales cover their expenditures. How much will the sales and expenditures be? How many cakes will they have sold?

System of equations

Answer 1

Let x be the number of cakes sold.

The cost of ingredients for x cakes is 3x.
The booth cost 52.
The sales will be 16x.
We know that the sales will cover the expenditures, so 16x = 3x + 52
Subtracting 3x from both sides, we get 13x = 52
Dividing both sides by 13, we get x = <<4=4>>4
The sales will be 16(4) = $<<16*4=64>>64
The expenditures will be 52 + 3(4) = $<<52+3*4=64>>64
The cooking club will have sold 4 cakes. Answer: \boxed{64}.