Betsy Is Shopping For A Cake And Cupcakes For A Birthday Party. Oakdale Bakery Charges \[$\$2.00\$\] Per Cupcake And \[$\$43.00\$\] For A Large Cake. Sally's Sweets Charges \[$\$3.00\$\] Per Cupcake And \[$\$33.00\$\]

Feb 28, 2025 by ADMIN 218 views

Betsy's Birthday Cake Conundrum: A Math Problem

Betsy is planning a birthday party and needs to decide which bakery to order her cake and cupcakes from. Oakdale Bakery charges $2.00 per cupcake and $43.00 for a large cake, while Sally's Sweets charges $3.00 per cupcake and $33.00 for a large cake. In this article, we will help Betsy make an informed decision by comparing the costs of the two bakeries.

Let's assume Betsy wants to order a certain number of cupcakes and a large cake from each bakery. We need to find the total cost of the order from each bakery. Let's denote the number of cupcakes as x and the number of large cakes as y.

Oakdale Bakery

The cost of the order from Oakdale Bakery can be calculated as follows:

Cost of cupcakes: $2.00x
Cost of large cakes: $43.00y
Total cost: $2.00x + $43.00y

Sally's Sweets

The cost of the order from Sally's Sweets can be calculated as follows:

Cost of cupcakes: $3.00x
Cost of large cakes: $33.00y
Total cost: $3.00x + $33.00y

To compare the costs of the two bakeries, we need to find the point at which the total cost of the order from each bakery is equal. This can be done by setting up an equation and solving for x and y.

Let's set up the equation:

$2.00x + $43.00y = $3.00x + $33.00y

Subtracting $2.00x from both sides gives:

$43.00y = $1.00x + $33.00y

Subtracting $33.00y from both sides gives:

$10.00y = $1.00x

Dividing both sides by $1.00 gives:

10y = x

So, the number of cupcakes is 10 times the number of large cakes.

In conclusion, Betsy should order 10 times as many cupcakes as large cakes from Oakdale Bakery to get the same total cost as Sally's Sweets. However, this is not the only factor to consider when making a decision. Betsy should also think about the quality of the cakes and cupcakes, the service provided by each bakery, and any other factors that may be important to her.

This problem has real-world applications in many areas, such as:

Business: Companies need to compare the costs of different suppliers and make informed decisions about which ones to use.
Finance: Individuals and businesses need to compare the costs of different financial products and make informed decisions about which ones to use.
Economics: Economists need to compare the costs of different goods and services and make informed decisions about which ones to produce and consume.

Here are some tips and tricks for solving this type of problem:

Read the problem carefully: Make sure you understand what is being asked and what information is given.
Identify the variables: Identify the variables in the problem and what they represent.
Set up the equation: Set up the equation based on the information given and the variables identified.
Solve the equation: Solve the equation to find the solution to the problem.
Check the solution: Check the solution to make sure it makes sense and is reasonable.

Here are some practice problems to help you practice solving this type of problem:

Problem 1: A bakery charges $2.00 per cupcake and $40.00 for a large cake. A rival bakery charges $3.00 per cupcake and $30.00 for a large cake. Find the point at which the total cost of the order from each bakery is equal.
Problem 2: A company needs to compare the costs of different suppliers for a certain product. The costs are as follows: Supplier A charges $10.00 per unit, Supplier B charges $12.00 per unit, and Supplier C charges $15.00 per unit. Find the point at which the total cost of the order from each supplier is equal.
Problem 3: An individual needs to compare the costs of different financial products. The costs are as follows: Product A charges $5.00 per month, Product B charges $7.00 per month, and Product C charges $10.00 per month. Find the point at which the total cost of the order from each product is equal.

In conclusion, this problem is a classic example of a linear programming problem. It requires the use of algebraic techniques to solve and has real-world applications in many areas. By following the tips and tricks outlined in this article, you should be able to solve this type of problem with ease.
Betsy's Birthday Cake Conundrum: A Math Problem Q&A

In our previous article, we helped Betsy make an informed decision about which bakery to order her cake and cupcakes from by comparing the costs of Oakdale Bakery and Sally's Sweets. In this article, we will answer some frequently asked questions about the problem and provide additional insights and tips.

Q: What is the main difference between Oakdale Bakery and Sally's Sweets?

A: The main difference between Oakdale Bakery and Sally's Sweets is the cost of their cupcakes and large cakes. Oakdale Bakery charges $2.00 per cupcake and $43.00 for a large cake, while Sally's Sweets charges $3.00 per cupcake and $33.00 for a large cake.

Q: How do I know which bakery to choose?

A: To choose which bakery to choose, you need to consider the number of cupcakes and large cakes you want to order. If you want to order a certain number of cupcakes and large cakes, you can use the equation we derived in our previous article to find the total cost of the order from each bakery.

Q: What if I want to order a different number of cupcakes and large cakes?

A: If you want to order a different number of cupcakes and large cakes, you can simply plug in the new numbers into the equation and solve for the total cost of the order from each bakery.

Q: Can I use this problem to compare the costs of other bakeries?

A: Yes, you can use this problem to compare the costs of other bakeries. Simply substitute the costs of the other bakeries into the equation and solve for the total cost of the order from each bakery.

Q: What if I want to order a different type of cake or cupcake?

A: If you want to order a different type of cake or cupcake, you will need to adjust the costs in the equation accordingly. For example, if you want to order a smaller cake, you will need to adjust the cost of the large cake in the equation.

Q: Can I use this problem to compare the costs of other products?

A: Yes, you can use this problem to compare the costs of other products. Simply substitute the costs of the other products into the equation and solve for the total cost of the order from each supplier.

Here are some additional tips and tricks for solving this type of problem:

Read the problem carefully: Make sure you understand what is being asked and what information is given.
Identify the variables: Identify the variables in the problem and what they represent.
Set up the equation: Set up the equation based on the information given and the variables identified.
Solve the equation: Solve the equation to find the solution to the problem.
Check the solution: Check the solution to make sure it makes sense and is reasonable.
Consider multiple scenarios: Consider multiple scenarios and adjust the equation accordingly.
Use a calculator: Use a calculator to help you solve the equation and check your solution.

This problem has real-world applications in many areas, such as:

Business: Companies need to compare the costs of different suppliers and make informed decisions about which ones to use.
Finance: Individuals and businesses need to compare the costs of different financial products and make informed decisions about which ones to use.
Economics: Economists need to compare the costs of different goods and services and make informed decisions about which ones to produce and consume.

Here are some practice problems to help you practice solving this type of problem:

Problem 1: A bakery charges $2.00 per cupcake and $40.00 for a large cake. A rival bakery charges $3.00 per cupcake and $30.00 for a large cake. Find the point at which the total cost of the order from each bakery is equal.
Problem 2: A company needs to compare the costs of different suppliers for a certain product. The costs are as follows: Supplier A charges $10.00 per unit, Supplier B charges $12.00 per unit, and Supplier C charges $15.00 per unit. Find the point at which the total cost of the order from each supplier is equal.
Problem 3: An individual needs to compare the costs of different financial products. The costs are as follows: Product A charges $5.00 per month, Product B charges $7.00 per month, and Product C charges $10.00 per month. Find the point at which the total cost of the order from each product is equal.