Question

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?

Answer 1

[AI-generated answer — Bot GPT 3.5]

Let's represent the number of cakes sold as "x".

The sales from selling x cakes can be represented as 16x.

The expenditures include the cost of the booth and the ingredients. The cost of the booth is $52 and the cost of the ingredients for each cake is $3. Therefore, the total expenditure can be represented as 52 + 3x.

According to the problem, the sales will cover the expenditures. So, we can set up the equation:

16x = 52 + 3x

To solve for x, we can use the substitution method.

First, subtract 3x from both sides of the equation:

16x - 3x = 52 + 3x - 3x

Simplifying, we get:

13x = 52

Next, divide both sides of the equation by 13 to solve for x:

x = 52 / 13

Simplifying, we get:

x = 4

Therefore, the cooking club will have sold 4 cakes.

To find the sales and expenditures, we can substitute the value of x into the equations:

Sales = 16x = 16 * 4 = $64
Expenditures = 52 + 3x = 52 + 3 * 4 = $64

Therefore, the sales and expenditures will both be $64. The cooking club will have sold 4 cakes.