Let's start by defining the variables:
Let's say:
x = number of cakes sold
y = total sales and expenditures
The cost of the booth is $52 and the cost of ingredients for each cake is $3. Therefore, the total expenditure is $52 + $3x.
The selling price of each cake is $16, so the total sales from selling x cakes is $16x.
According to the problem, the club members will sell enough cakes so that their sales cover their expenditures. Mathematically, this is represented by the equation:
sales = expenditures
$16x = $52 + $3x
To solve this equation, we need to isolate x. We can do this by subtracting $3x from both sides of the equation:
$16x - $3x = $52 + $3x - $3x
$13x = $52
Now we can solve for x by dividing both sides of the equation by $13:
x = $52 / $13
x = 4
Therefore, the club members will have sold 4 cakes.
To calculate the total sales and expenditures (y), we can substitute the value of x into one of the original equations. Let's use the equation for expenditures:
y = $52 + $3x
y = $52 + $3(4)
y = $52 + $12
y = $64
Therefore, the total sales and expenditures will be $64. The club members will have sold 4 cakes.