Demonstration of the substitution method is required for this assessment. Show all work!
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? Solve for y
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.