Your class has decided to have a bake sale for a fund raiser. The students de- cided on the following prices for baked goods.
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?
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.
Part A:
To provide the math teacher with the information she needs to make 120 cookies, we can use the ratio of 3 cookies for $1.00. This means that for every 3 cookies, the cost is $1.00. Therefore, we can set up a proportion to find the number of cookies needed:
3 cookies / $1.00 = 120 cookies / x
Cross-multiplying, we get:
3x = 120
x = 40
So, the math teacher will need to make 40 batches of 3 cookies, which totals 120 cookies.
Part B:
To raise at least $150.00 for the fundraiser, we need to calculate the quantities of each baked good that will generate this amount.
Let's calculate the cost per item for each type of baked good:
- Brownies: 4 brownies for $1.25, so each brownie costs $1.25 / 4 = $0.3125
- Cupcakes: 5 cupcakes for $2.50, so each cupcake costs $2.50 / 5 = $0.50
- Cookies: 3 cookies for $1.00, so each cookie costs $1.00 / 3 = $0.3333 (rounded to 4 decimal places)
- Cake: 1 cake for $4.50, so each cake costs $4.50
- Pie: 1 pie for $5.00, so each pie costs $5.00
- Popcorn Balls: 2 popcorn balls for $0.75, so each popcorn ball costs $0.75 / 2 = $0.375
Now, let's calculate the quantity of each baked good needed to reach the goal of $150.00:
- Brownies: $150.00 / $0.3125 = 480 brownies (rounded to the nearest whole number)
- Cupcakes: $150.00 / $0.50 = 300 cupcakes
- Cookies: $150.00 / $0.3333 = 450 cookies (rounded to the nearest whole number)
- Cakes: $150.00 / $4.50 = 33.3333 cakes (rounded to the nearest whole number)
- Pies: $150.00 / $5.00 = 30 pies
- Popcorn Balls: $150.00 / $0.375 = 400 popcorn balls
Therefore, to raise at least $150.00, you recommend having:
- 480 brownies
- 300 cupcakes
- 450 cookies
- 34 cakes (rounded up)
- 30 pies
- 400 popcorn balls
Part C:
The math teacher wants 6 of each item. Let's calculate the cost of her purchase:
- Brownies: 6 brownies * $0.3125 = $1.875
- Cupcakes: 6 cupcakes * $0.50 = $3.00
- Cookies: 6 cookies * $0.3333 = $2.00 (rounded to 2 decimal places)
- Cakes: 6 cakes * $4.50 = $27.00
- Pies: 6 pies * $5.00 = $30.00
- Popcorn Balls: 6 popcorn balls * $0.375 = $2.25
Therefore, the math teacher's purchase will cost $1.875 + $3.00 + $2.00 + $27.00 + $30.00 + $2.25 = $66.125. Rounded to two decimal places, her purchase comes to $66.13.