Fiona Bought Some Socks That Cost $\$4.95$ For Each Pair And Some Belts That Cost $\$6.55$ Each. Fiona Spent $\$27.95$ In All. Let $a$ Represent The Number Of Pairs Of Socks Purchased And $b$ The Number Of

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Introduction

In this article, we will delve into a real-world scenario involving a young shopper named Fiona, who purchased socks and belts from a store. The prices of the items and the total amount spent will be used to create a mathematical equation, which we will then solve to find the number of pairs of socks and belts purchased. This problem is a great example of how mathematics can be applied to everyday situations, making it a fun and engaging way to learn and practice mathematical concepts.

The Problem

Fiona bought some socks that cost $4.95\$4.95 for each pair and some belts that cost $6.55\$6.55 each. Fiona spent $27.95\$27.95 in all. Let aa represent the number of pairs of socks purchased and bb the number of belts purchased. We can create an equation to represent the total amount spent by Fiona.

Equation

The total amount spent by Fiona can be represented by the equation:

4.95a+6.55b=27.954.95a + 6.55b = 27.95

This equation states that the total amount spent is equal to the sum of the cost of the socks and the cost of the belts.

Solving the Equation

To solve for the number of pairs of socks and belts purchased, we can use the method of substitution or elimination. In this case, we will use the substitution method.

First, we can isolate one of the variables by subtracting the product of the other variable and its coefficient from both sides of the equation. Let's isolate aa by subtracting 6.55b6.55b from both sides:

4.95a=27.95−6.55b4.95a = 27.95 - 6.55b

Next, we can divide both sides of the equation by 4.954.95 to solve for aa:

a=27.95−6.55b4.95a = \frac{27.95 - 6.55b}{4.95}

Finding the Number of Pairs of Socks Purchased

Now that we have the equation for aa, we can substitute different values of bb to find the corresponding values of aa. However, we need to find a value of bb that makes the equation true. Let's try to find a value of bb that is a whole number, as it is more likely that Fiona purchased a whole number of belts.

Trial and Error

We can start by trying different values of bb and see if we can find a value that makes the equation true. Let's try b=1b = 1:

a=27.95−6.55(1)4.95a = \frac{27.95 - 6.55(1)}{4.95}

a=27.95−6.554.95a = \frac{27.95 - 6.55}{4.95}

a=21.404.95a = \frac{21.40}{4.95}

a=4.32a = 4.32

Since aa is not a whole number, we need to try another value of bb. Let's try b=2b = 2:

a=27.95−6.55(2)4.95a = \frac{27.95 - 6.55(2)}{4.95}

a=27.95−13.104.95a = \frac{27.95 - 13.10}{4.95}

a=14.854.95a = \frac{14.85}{4.95}

a=3.00a = 3.00

Now that we have a whole number value for aa, we can conclude that Fiona purchased 3 pairs of socks.

Finding the Number of Belts Purchased

Now that we know the number of pairs of socks purchased, we can substitute this value into the equation to find the number of belts purchased. Let's substitute a=3a = 3 into the equation:

4.95(3)+6.55b=27.954.95(3) + 6.55b = 27.95

14.85+6.55b=27.9514.85 + 6.55b = 27.95

6.55b=27.95−14.856.55b = 27.95 - 14.85

6.55b=13.106.55b = 13.10

b=13.106.55b = \frac{13.10}{6.55}

b=2.00b = 2.00

Now that we have a whole number value for bb, we can conclude that Fiona purchased 2 belts.

Conclusion

In this article, we used a real-world scenario to create a mathematical equation and solve for the number of pairs of socks and belts purchased. We used the substitution method to solve for the variables and found that Fiona purchased 3 pairs of socks and 2 belts. This problem is a great example of how mathematics can be applied to everyday situations, making it a fun and engaging way to learn and practice mathematical concepts.

Real-World Applications

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

  • Shopping: When shopping, we often need to calculate the total cost of items and make decisions based on our budget.
  • Cooking: When cooking, we need to measure ingredients and calculate the total cost of the recipe.
  • Finance: When managing finances, we need to calculate interest rates, taxes, and other financial metrics.

Mathematical Concepts

This problem involves several mathematical concepts, such as:

  • Linear Equations: We used a linear equation to represent the total amount spent by Fiona.
  • Substitution Method: We used the substitution method to solve for the variables.
  • Trial and Error: We used trial and error to find a value of bb that makes the equation true.

Tips and Tricks

Here are some tips and tricks to help you solve this problem:

  • Read the problem carefully: Make sure you understand the problem and what is being asked.
  • Use the substitution method: The substitution method is a powerful tool for solving linear equations.
  • Try different values: Don't be afraid to try different values of bb to find a value that makes the equation true.

Conclusion

Introduction

In our previous article, we explored a real-world scenario involving a young shopper named Fiona, who purchased socks and belts from a store. We created a mathematical equation to represent the total amount spent by Fiona and solved for the number of pairs of socks and belts purchased. In this article, we will answer some frequently asked questions related to this problem.

Q&A

Q: What is the total amount spent by Fiona?

A: The total amount spent by Fiona is $27.95\$27.95.

Q: How many pairs of socks did Fiona purchase?

A: Fiona purchased 3 pairs of socks.

Q: How many belts did Fiona purchase?

A: Fiona purchased 2 belts.

Q: What is the cost of each pair of socks?

A: The cost of each pair of socks is $4.95\$4.95.

Q: What is the cost of each belt?

A: The cost of each belt is $6.55\$6.55.

Q: How did you solve for the number of pairs of socks and belts purchased?

A: We used the substitution method to solve for the variables. We isolated one of the variables by subtracting the product of the other variable and its coefficient from both sides of the equation. Then, we divided both sides of the equation by the coefficient of the isolated variable to solve for the variable.

Q: What is the significance of this problem?

A: This problem is a great example of how mathematics can be applied to everyday situations. It involves several mathematical concepts, such as linear equations, substitution method, and trial and error. It also has many real-world applications, such as shopping, cooking, and finance.

Q: How can I apply this problem to my everyday life?

A: You can apply this problem to your everyday life by using it to calculate the total cost of items, make decisions based on your budget, and manage your finances.

Q: What are some tips and tricks for solving this problem?

A: Some tips and tricks for solving this problem include:

  • Read the problem carefully: Make sure you understand the problem and what is being asked.
  • Use the substitution method: The substitution method is a powerful tool for solving linear equations.
  • Try different values: Don't be afraid to try different values of bb to find a value that makes the equation true.

Conclusion

In conclusion, this problem is a great example of how mathematics can be applied to everyday situations. We used a real-world scenario to create a mathematical equation and solve for the number of pairs of socks and belts purchased. We answered some frequently asked questions related to this problem and provided some tips and tricks for solving it. This problem has many real-world applications and involves several mathematical concepts, such as linear equations, substitution method, and trial and error.

Real-World Applications

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

  • Shopping: When shopping, we often need to calculate the total cost of items and make decisions based on our budget.
  • Cooking: When cooking, we need to measure ingredients and calculate the total cost of the recipe.
  • Finance: When managing finances, we need to calculate interest rates, taxes, and other financial metrics.

Mathematical Concepts

This problem involves several mathematical concepts, such as:

  • Linear Equations: We used a linear equation to represent the total amount spent by Fiona.
  • Substitution Method: We used the substitution method to solve for the variables.
  • Trial and Error: We used trial and error to find a value of bb that makes the equation true.

Tips and Tricks

Here are some tips and tricks to help you solve this problem:

  • Read the problem carefully: Make sure you understand the problem and what is being asked.
  • Use the substitution method: The substitution method is a powerful tool for solving linear equations.
  • Try different values: Don't be afraid to try different values of bb to find a value that makes the equation true.

Conclusion

In conclusion, this problem is a great example of how mathematics can be applied to everyday situations. We used a real-world scenario to create a mathematical equation and solve for the number of pairs of socks and belts purchased. We answered some frequently asked questions related to this problem and provided some tips and tricks for solving it. This problem has many real-world applications and involves several mathematical concepts, such as linear equations, substitution method, and trial and error.