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?
What are the equations
Let's assume the number of cakes they will sell is 'x'.
The total cost for the booth is $52.
The total cost for the ingredients for 'x' cakes is 3x.
The total sales for 'x' cakes will be 16x.
The equation for the club members' expenditures is:
Cost of the booth + Cost of ingredients = $52 + 3x
The equation for the club members' sales is:
Sales from cakes = 16x
To find the number of cakes they will have sold when their sales cover their expenditures, we equate the two equations:
16x = 52 + 3x
Simplifying the equation:
16x - 3x = 52
13x = 52
x = 52/13
x = 4
Therefore, they will have sold 4 cakes when their sales cover their expenditures.
To find the amount of sales and expenditures, we substitute the value of x into the respective equations:
Sales = 16x = 16 * 4 = $<<16*4=64>>64
Expenditures = $52 + 3x = $52 + 3 * 4 = $52 + $12 = $<<52+3*4=64>>64
So, the sales will be $64 and the expenditures will also be $64.