Fiona And Her Friends Went To A Smoothie Shop. They Ordered Three Strawberry Smoothies And Two Protein Shakes For A Total Of $\$24.00$. Last Week, They Ordered One Strawberry Smoothie And Four Protein Shakes For A Total Of $\$25.50$.

Feb 27, 2025 by ADMIN 234 views

Fiona's Smoothie Shop Adventure: A Math Problem

Fiona and her friends are regular customers at a local smoothie shop. They have been visiting the shop for a while now, and their orders have been quite consistent. In this article, we will explore the math behind their orders and try to understand the relationship between the number of smoothies and protein shakes they ordered and the total amount they paid.

Fiona and her friends went to the smoothie shop and ordered three strawberry smoothies and two protein shakes for a total of $\$24.00$ . Last week, they ordered one strawberry smoothie and four protein shakes for a total of $\$25.50$ . We need to find the cost of one strawberry smoothie and one protein shake.

Let's denote the cost of one strawberry smoothie as $x$ and the cost of one protein shake as $y$ . We can set up two equations based on the information given:

$3x + 2y = 24.00$
$x + 4y = 25.50$

We can solve this system of equations using the method of substitution or elimination. Let's use the elimination method. We can multiply the second equation by 3 to get:

$3x + 12y = 76.50$

Now, we can subtract the first equation from this new equation to get:

$10y = 52.50$

Dividing both sides by 10, we get:

$y = 5.25$

Now that we have found the cost of one protein shake, we can substitute this value into one of the original equations to find the cost of one strawberry smoothie. Let's use the first equation:

$3x + 2(5.25) = 24.00$

Simplifying this equation, we get:

$3x + 10.50 = 24.00$

Subtracting 10.50 from both sides, we get:

$3x = 13.50$

Dividing both sides by 3, we get:

$x = 4.50$

Fiona and her friends ordered three strawberry smoothies and two protein shakes for a total of $\$24.00$ , and last week, they ordered one strawberry smoothie and four protein shakes for a total of $\$25.50$ . We were able to find the cost of one strawberry smoothie and one protein shake using the method of elimination. The cost of one strawberry smoothie is $\$4.50$ , and the cost of one protein shake is $\$5.25$ .

This problem may seem simple, but it has real-world applications in various fields, such as:

Business: Understanding the cost of different products and services is crucial for businesses to make informed decisions about pricing and inventory management.
Economics: The concept of opportunity cost is closely related to the idea of cost-benefit analysis, which is essential for making decisions in economics.
Mathematics: Solving systems of equations is a fundamental concept in mathematics, and it has numerous applications in various fields, including physics, engineering, and computer science.

Use the elimination method: When solving systems of equations, the elimination method can be a powerful tool for finding the solution.
Check your work: Always check your work to ensure that you have found the correct solution.
Practice, practice, practice: The more you practice solving systems of equations, the more comfortable you will become with the concept.

Fiona and her friends' smoothie shop adventure may seem like a simple math problem, but it has real-world applications and can help us understand the concept of cost-benefit analysis. By solving systems of equations, we can find the cost of different products and services, which is essential for making informed decisions in various fields.
Fiona's Smoothie Shop Adventure: A Math Problem Q&A

In our previous article, we explored the math behind Fiona and her friends' smoothie shop orders. We found the cost of one strawberry smoothie and one protein shake using the method of elimination. In this article, we will answer some frequently asked questions about the problem and provide additional insights.

Q: What is the cost of one strawberry smoothie? A: The cost of one strawberry smoothie is $\$4.50$ .

Q: What is the cost of one protein shake? A: The cost of one protein shake is $\$5.25$ .

Q: How did you find the cost of one strawberry smoothie and one protein shake? A: We used the method of elimination to solve the system of equations. We multiplied the second equation by 3 to get $3x + 12y = 76.50$ , and then we subtracted the first equation from this new equation to get $10y = 52.50$ . We then divided both sides by 10 to get $y = 5.25$ . Finally, we substituted this value into one of the original equations to find the cost of one strawberry smoothie.

Q: What is the relationship between the number of smoothies and protein shakes ordered and the total amount paid? A: The relationship between the number of smoothies and protein shakes ordered and the total amount paid is given by the system of equations:

$3x + 2y = 24.00$
$x + 4y = 25.50$

Q: Can you explain the concept of opportunity cost? A: Opportunity cost is the cost of choosing one option over another. In the context of Fiona and her friends' smoothie shop orders, the opportunity cost of choosing one strawberry smoothie over one protein shake is the difference in cost between the two options.

Q: How can you apply the concept of cost-benefit analysis to real-world situations? A: Cost-benefit analysis is a decision-making tool that involves weighing the costs and benefits of different options. In the context of Fiona and her friends' smoothie shop orders, cost-benefit analysis would involve considering the cost of one strawberry smoothie and one protein shake and comparing it to the benefits of choosing one option over the other.

Q: What are some real-world applications of solving systems of equations? A: Solving systems of equations has numerous real-world applications, including:

Business: Understanding the cost of different products and services is crucial for businesses to make informed decisions about pricing and inventory management.
Economics: The concept of opportunity cost is closely related to the idea of cost-benefit analysis, which is essential for making decisions in economics.
Mathematics: Solving systems of equations is a fundamental concept in mathematics, and it has numerous applications in various fields, including physics, engineering, and computer science.

Fiona and her friends' smoothie shop adventure may seem like a simple math problem, but it has real-world applications and can help us understand the concept of cost-benefit analysis. By solving systems of equations, we can find the cost of different products and services, which is essential for making informed decisions in various fields. We hope this Q&A article has provided additional insights and helped you understand the problem better.

Use the elimination method: When solving systems of equations, the elimination method can be a powerful tool for finding the solution.
Check your work: Always check your work to ensure that you have found the correct solution.
Practice, practice, practice: The more you practice solving systems of equations, the more comfortable you will become with the concept.

Math textbooks: For more information on solving systems of equations, check out your math textbook or online resources.
Online tutorials: Websites like Khan Academy and Mathway offer video tutorials and interactive exercises to help you practice solving systems of equations.
Practice problems: Try solving more practice problems to reinforce your understanding of the concept.