Sara Makes And Sells Bracelets. She Bought Material For $ 28.50 \$28.50 $28.50 And Used It All To Make 15 Bracelets. Sara Used The Equation 15 X − 28.50 = 99 15x - 28.50 = 99 15 X − 28.50 = 99 To Determine X X X , The Amount She Should Charge For Each Bracelet To Make A

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Sara's Bracelet Business: A Mathematical Approach to Pricing

Sara is a crafty entrepreneur who has started a small business selling handmade bracelets. With a passion for creating unique and beautiful pieces, Sara has invested in materials worth $28.50\$28.50 to make 15 bracelets. However, she is now faced with the challenge of determining the optimal price for each bracelet to ensure a profit. In this article, we will delve into the mathematical equation that Sara has used to determine the price of each bracelet, and explore the underlying concepts that make this equation work.

Sara has used the equation 15x−28.50=9915x - 28.50 = 99 to determine the amount she should charge for each bracelet. This equation is based on the concept of revenue, which is the total amount of money earned from selling a product. In this case, the revenue is the product of the number of bracelets sold (15) and the price of each bracelet (x). The equation can be broken down into two parts:

  • The first part, 15x15x, represents the total revenue from selling 15 bracelets at a price of x dollars each.
  • The second part, −28.50-28.50, represents the cost of materials used to make the 15 bracelets.
  • The third part, 9999, represents the desired profit that Sara wants to make.

To solve the equation, we need to isolate the variable x, which represents the price of each bracelet. We can do this by adding 28.50 to both sides of the equation, which gives us:

15x=99+28.5015x = 99 + 28.50

Simplifying the right-hand side of the equation, we get:

15x=127.5015x = 127.50

Next, we can divide both sides of the equation by 15 to solve for x:

x=127.5015x = \frac{127.50}{15}

Simplifying the right-hand side of the equation, we get:

x=8.50x = 8.50

So, what does this mean for Sara's business? The solution to the equation, x = 8.50, tells us that Sara should charge $8.50\$8.50 for each bracelet to make a profit of $99\$99. This means that Sara will earn a total of $127.50\$127.50 from selling 15 bracelets at this price.

In conclusion, Sara's use of the equation 15x−28.50=9915x - 28.50 = 99 has provided her with a mathematical approach to determining the price of each bracelet. By solving the equation, Sara has been able to determine the optimal price for each bracelet, which will help her to make a profit of $99\$99. This example illustrates the importance of mathematical modeling in business decision-making, and highlights the need for entrepreneurs to use mathematical tools to make informed decisions.

The concept of revenue and profit is not limited to Sara's bracelet business. In fact, it is a fundamental concept in business and economics. Companies use mathematical models to determine the optimal price for their products, taking into account factors such as production costs, market demand, and competition.

The equation 15x−28.50=9915x - 28.50 = 99 involves several mathematical concepts, including:

  • Linear equations: The equation is a linear equation, which means that it can be represented graphically as a straight line.
  • Variables: The equation involves a variable, x, which represents the price of each bracelet.
  • Constants: The equation involves constants, 15 and 28.50, which represent the number of bracelets sold and the cost of materials, respectively.
  • Operations: The equation involves several mathematical operations, including addition, subtraction, and division.

When working with linear equations, it is essential to follow the order of operations (PEMDAS):

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

By following these tips and tricks, you can simplify complex equations and solve for variables with ease.

Try solving the following practice problems to reinforce your understanding of linear equations:

  1. Solve the equation 2x+5=112x + 5 = 11 for x.
  2. Solve the equation x−3=7x - 3 = 7 for x.
  3. Solve the equation 4x=244x = 24 for x.

In conclusion, Sara's use of the equation 15x−28.50=9915x - 28.50 = 99 has provided her with a mathematical approach to determining the price of each bracelet. By solving the equation, Sara has been able to determine the optimal price for each bracelet, which will help her to make a profit of $99\$99. This example illustrates the importance of mathematical modeling in business decision-making, and highlights the need for entrepreneurs to use mathematical tools to make informed decisions.
Sara's Bracelet Business: A Mathematical Approach to Pricing - Q&A

In our previous article, we explored the mathematical equation that Sara used to determine the price of each bracelet to make a profit of $99\$99. We also discussed the underlying concepts that make this equation work, including linear equations, variables, constants, and operations. In this article, we will answer some frequently asked questions (FAQs) related to Sara's bracelet business and the mathematical equation used to determine the price of each bracelet.

Q: What is the main goal of Sara's bracelet business? A: The main goal of Sara's bracelet business is to make a profit of $99\$99 by selling 15 bracelets at a price that will cover the cost of materials and provide a desired profit.

Q: What is the equation that Sara used to determine the price of each bracelet? A: The equation that Sara used is 15x−28.50=9915x - 28.50 = 99, where x represents the price of each bracelet.

Q: What is the significance of the number 15 in the equation? A: The number 15 in the equation represents the number of bracelets that Sara made and wants to sell.

Q: What is the significance of the number 28.50 in the equation? A: The number 28.50 in the equation represents the cost of materials used to make the 15 bracelets.

Q: What is the significance of the number 99 in the equation? A: The number 99 in the equation represents the desired profit that Sara wants to make.

Q: How did Sara solve the equation to determine the price of each bracelet? A: Sara solved the equation by adding 28.50 to both sides of the equation, which gave her 15x=127.5015x = 127.50. She then divided both sides of the equation by 15 to solve for x, which gave her x = 8.50.

Q: What does the solution x = 8.50 mean for Sara's business? A: The solution x = 8.50 means that Sara should charge $8.50\$8.50 for each bracelet to make a profit of $99\$99.

Q: What are some real-world applications of the concept of revenue and profit? A: The concept of revenue and profit is not limited to Sara's bracelet business. In fact, it is a fundamental concept in business and economics. Companies use mathematical models to determine the optimal price for their products, taking into account factors such as production costs, market demand, and competition.

Q: What are some tips and tricks for working with linear equations? A: When working with linear equations, it is essential to follow the order of operations (PEMDAS):

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: What are some practice problems that can help reinforce understanding of linear equations? A: Try solving the following practice problems to reinforce your understanding of linear equations:

  1. Solve the equation 2x+5=112x + 5 = 11 for x.
  2. Solve the equation x−3=7x - 3 = 7 for x.
  3. Solve the equation 4x=244x = 24 for x.

In conclusion, Sara's use of the equation 15x−28.50=9915x - 28.50 = 99 has provided her with a mathematical approach to determining the price of each bracelet. By solving the equation, Sara has been able to determine the optimal price for each bracelet, which will help her to make a profit of $99\$99. This example illustrates the importance of mathematical modeling in business decision-making, and highlights the need for entrepreneurs to use mathematical tools to make informed decisions.