3. In your industrial oven, you bake two baking sheets with 12 scones each, two baking sheets with 20 cookies each, and one baking sheet with 2 scones and 10 cookies.

a. Write an expression that illustrates the total cost of all baked goods in the scenario above using the variable s to represent the cost of scones, and the variable c to represent the cost of cookies. Simplify your expression by combining like terms.

b. Imagine you have decided to price the scones at $2.28 each and the cookies at $1.19 each. How much total revenue would result from selling all the scones and cookies baked in the oven at one time?

c. Yesterday your store earned $797.30 just from the sale of cookies. Write and solve an equation that represents how many cookies were sold.

a. The expression that illustrates the total cost of all baked goods can be calculated by multiplying the number of scones and cookies on each baking sheet by their respective costs and then adding them all together. Let's break it down:

For the two baking sheets with 12 scones each, the cost would be 2 * 12 * s = 24s.
For the two baking sheets with 20 cookies each, the cost would be 2 * 20 * c = 40c.
For the baking sheet with 2 scones and 10 cookies, the cost would be 2 * s + 10 * c.

Adding all these costs together, the expression for the total cost of all baked goods is: 24s + 40c + 2s + 10c.

To simplify the expression, we can combine like terms: 24s + 2s + 40c + 10c becomes 26s + 50c.

b. If each scone is priced at $2.28 and each cookie is priced at $1.19, we can calculate the total revenue by multiplying the number of scones and cookies by their respective prices and then adding them all together. Let's break it down:

For the two baking sheets with 12 scones each, the revenue would be 2 * 12 * $2.28 = $54.72.
For the two baking sheets with 20 cookies each, the revenue would be 2 * 20 * $1.19 = $47.60.
For the baking sheet with 2 scones and 10 cookies, the revenue would be 2 * $2.28 + 10 * $1.19 = $6.56 + $11.90 = $18.46.

Adding all these revenues together, the total revenue from selling all the baked goods would be: $54.72 + $47.60 + $18.46.

Adding these amounts together, the total revenue would be: $54.72 + $47.60 + $18.46 = $120.78.

c. Let's assume the number of cookies sold is represented by the variable x. Since the price of a cookie is $1.19, the total revenue from selling x cookies can be calculated as $1.19 * x.

Given that the store earned $797.30 from cookie sales, we can set up the equation:

$1.19 * x = $797.30.

To solve for x, we can divide both sides of the equation by $1.19:

x = $797.30 / $1.19.

Using a calculator, we can find that x ≈ 670.59.

Therefore, approximately 670 cookies were sold yesterday.

a. To illustrate the total cost of all baked goods in the scenario above, we need to determine the cost of each item and then multiply that by the number of items.

Let's say the cost of each scone is represented by the variable s, and the cost of each cookie is represented by the variable c.

For the first baking sheet with 12 scones, the cost would be 12s.
For the second baking sheet with 20 cookies, the cost would be 20c.
For the third baking sheet with 2 scones and 10 cookies, the cost would be 2s + 10c.

To find the total cost, we need to add up the costs of all the baking sheets:

Total cost = (12s + 20c) + (12s + 20c) + (2s + 10c)

Combining like terms, we get:

Total cost = 26s + 40c + 2s + 10c

Simplifying further, we have:

Total cost = 28s + 50c

b. If we have decided to price the scones at $2.28 each and the cookies at $1.19 each, we can substitute these values into the expression we derived.

Total revenue = (28 * $2.28) + (50 * $1.19)

Calculating this, we get:

Total revenue = $63.84 + $59.50

Total revenue = $123.34

Therefore, the total revenue from selling all the scones and cookies baked in the oven at one time would be $123.34.

c. To calculate how many cookies were sold when the store earned $797.30 just from the sale of cookies, we need to represent the number of cookies sold by a variable, let's call it x.

The equation representing the sale of cookies is:

Revenue from cookies = cost per cookie * number of cookies sold

797.30 = $1.19 * x

To solve for x, we divide both sides of the equation by $1.19:

x = 797.30 / $1.19

Calculating this, we find:

x = 670

Therefore, 670 cookies were sold yesterday.