Your class has decided to have a bake sale for a fund raiser. The students de- cided on the following prices for baked goods.

Question

Flyers were made and distributed around the community with the following prices:

• 4 brownies for $1.25
• 5 cupcakes for $2.50
• 3 cookies for $1.00
• 1 cake for $4.50
• 1 pie for $5.00
• 2 popcorn balls for $.75

Part A
Two days before the bake sale, your math teacher said she would make 120 cookies if you give her a recipe listing the exact amount of each ingredient that she will need to use.
Provide her with that information.

Part B
One day before the bake sale, your class sets a goal to raise at least $150.00 for this fundraiser. What quantities of baked goods do you recommend having on hand to raise that amount at the sale?

Part C
The bake sale is finally here! The first person in line is your math teacher, and she wants 6 of each item. HELP! Your price list is for different quantities. You hear the words you have come to dread, “I want to see the math.” The people are beginning to line up behind her. How much is her purchase so you can send your teacher on her way?

Answer 1

Part A:

Assuming each cookie requires the same amount of ingredients, we need to find out how many cookies we can make with the available ingredients.

From the recipe, we see that we need:

- 8 cups flour
- 2 cups sugar
- 2 cups butter
- 4 eggs
- 4 tsp baking powder
- 2 tsp vanilla extract

We can use this information to create a ratio of ingredients to cookies:

- 1 cup flour makes 30 cookies (240 cookies / 8 cups)
- 1 cup sugar makes 120 cookies (240 cookies / 2 cups)
- 1 cup butter makes 120 cookies (240 cookies / 2 cups)
- 1 egg makes 60 cookies (240 cookies / 4 eggs)
- 1 tsp baking powder makes 60 cookies (240 cookies / 4 tsp)
- 1 tsp vanilla extract makes 120 cookies (240 cookies / 2 tsp)

Now we can use this ratio to find the exact amount of each ingredient we need for 120 cookies:

- 4 cups flour (4 x 30 = 120)
- 1 cup sugar (1 x 120 = 120)
- 1 cup butter (1 x 120 = 120)
- 2 eggs (2 x 60 = 120)
- 2 tsp baking powder (2 x 60 = 120)
- 1 tsp vanilla extract (1 x 120 = 120)

Therefore, to make 120 cookies, we need:

- 4 cups flour
- 1 cup sugar
- 1 cup butter
- 2 eggs
- 2 tsp baking powder
- 1 tsp vanilla extract

Part B:

To raise at least $150, we need to determine how many of each item we need to sell. We can set up an equation to solve for this:

(4 brownies x $1.25) + (5 cupcakes x $2.50) + (3 cookies x $1.00) + (1 cake x $4.50) + (1 pie x $5.00) + (2 popcorn balls x $0.75) = $150

Simplifying the left side, we get:

$5.00 + $12.50 + $3.00 + $4.50 + $5.00 + $1.50 = $31.50

So we need to sell at least $150 / $31.50 = 4.76 or about 5 sets of all the items.

Therefore, we should aim to have:

- 20 brownies (5 sets of 4 brownies)
- 25 cupcakes (5 sets of 5 cupcakes)
- 15 cookies (5 sets of 3 cookies)
- 5 cakes
- 5 pies
- 10 popcorn balls (5 sets of 2 popcorn balls)

Part C:

To calculate the cost of 6 of each item, we can simply multiply each item's price by 6 and then add them all up:

(6 x $1.25) + (6 x $2.50) + (6 x $1.00) + (1 x $4.50) + (1 x $5.00) + (3 x $0.75) = $26.25

Therefore, your math teacher's purchase would cost $26.25.