Darcy Gave Her Beauty Technician A $4.80 Tip. The Tip Was 5% Of The Cost Of The Procedure. Write An Equation To Find \[$ B \$\], The Cost Of The Procedure.If All Percents Are Expressed As Decimals, The Equation Can Be Used To Find \[$ B

by ADMIN 237 views

Understanding the Problem: A Math Puzzle

In this article, we will delve into a mathematical problem presented by Darcy, who gave her beauty technician a $4.80 tip. The tip was 5% of the cost of the procedure. Our goal is to write an equation to find { b $}$, the cost of the procedure.

The Problem: A Real-World Scenario

Darcy's situation is a real-world example of how math is used in everyday life. When she gave her beauty technician a $4.80 tip, she was essentially paying 5% of the cost of the procedure. This means that the tip is a fraction of the total cost, and we need to find the total cost.

Expressing Percentages as Decimals

To solve this problem, we need to express the percentage as a decimal. A percentage is a way of expressing a value as a fraction of 100. To convert a percentage to a decimal, we divide by 100. In this case, 5% is equal to 0.05.

Writing the Equation

Now that we have expressed the percentage as a decimal, we can write the equation to find the cost of the procedure. Let's call the cost of the procedure { b $}$. The tip is 5% of the cost, which is equal to 0.05 times the cost. We know that the tip is $4.80, so we can set up the equation:

0.05 * { b $}$ = 4.80

Solving the Equation

To solve for { b $}$, we need to isolate the variable. We can do this by dividing both sides of the equation by 0.05. This will give us:

{ b $}$ = 4.80 / 0.05

Calculating the Cost

Now that we have the equation, we can calculate the cost of the procedure. We can use a calculator to divide 4.80 by 0.05, or we can do it manually by dividing 480 by 5.

{ b $}$ = 96

Conclusion

In this article, we have written an equation to find the cost of a procedure based on a 5% tip. We expressed the percentage as a decimal and used it to set up the equation. We then solved for the variable and calculated the cost of the procedure. This problem is a great example of how math is used in real-world scenarios, and how it can be applied to solve everyday problems.

Real-World Applications

This problem has many real-world applications. For example, if you are a business owner, you may need to calculate the cost of a procedure based on a percentage of the total cost. This can help you determine the profitability of a service or product. Additionally, if you are a consumer, you may need to calculate the cost of a procedure based on a percentage of the total cost. This can help you make informed decisions about your spending.

Mathematical Concepts

This problem involves several mathematical concepts, including:

  • Percentages: We expressed the percentage as a decimal and used it to set up the equation.
  • Decimals: We converted the percentage to a decimal and used it to solve the equation.
  • Equations: We set up and solved an equation to find the cost of the procedure.
  • Variables: We isolated the variable and solved for it.

Tips and Tricks

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

  • Read the problem carefully: Make sure you understand what the problem is asking for.
  • Express percentages as decimals: This will make it easier to set up and solve the equation.
  • Use a calculator: If you are having trouble solving the equation manually, use a calculator to help you.
  • Check your work: Make sure you have solved the equation correctly by checking your work.

Conclusion

In conclusion, this problem is a great example of how math is used in real-world scenarios. We wrote an equation to find the cost of a procedure based on a 5% tip, expressed the percentage as a decimal, and solved for the variable. This problem has many real-world applications and involves several mathematical concepts, including percentages, decimals, equations, and variables. By following the tips and tricks outlined in this article, you can solve this problem and many others like it.
Q&A: Understanding the Problem and Solving the Equation

In our previous article, we delved into a mathematical problem presented by Darcy, who gave her beauty technician a $4.80 tip. The tip was 5% of the cost of the procedure. Our goal was to write an equation to find { b $}$, the cost of the procedure. In this article, we will answer some frequently asked questions about the problem and provide additional guidance on how to solve it.

Q: What is the problem asking for?

A: The problem is asking for the cost of the procedure, denoted by { b $}$. We are given that the tip is 5% of the cost, and we need to find the total cost.

Q: How do I express the percentage as a decimal?

A: To express a percentage as a decimal, you divide by 100. In this case, 5% is equal to 0.05.

Q: What is the equation to find the cost of the procedure?

A: The equation is:

0.05 * { b $}$ = 4.80

Q: How do I solve the equation?

A: To solve for { b $}$, you need to isolate the variable. You can do this by dividing both sides of the equation by 0.05.

Q: What is the cost of the procedure?

A: To find the cost of the procedure, you need to divide 4.80 by 0.05. This will give you:

{ b $}$ = 96

Q: What if I get a different answer?

A: If you get a different answer, double-check your work. Make sure you have expressed the percentage as a decimal correctly and that you have solved the equation correctly.

Q: Can I use a calculator to solve the equation?

A: Yes, you can use a calculator to solve the equation. This can be helpful if you are having trouble solving the equation manually.

Q: What are some real-world applications of this problem?

A: This problem has many real-world applications. For example, if you are a business owner, you may need to calculate the cost of a procedure based on a percentage of the total cost. This can help you determine the profitability of a service or product. Additionally, if you are a consumer, you may need to calculate the cost of a procedure based on a percentage of the total cost. This can help you make informed decisions about your spending.

Q: What mathematical concepts are involved in this problem?

A: This problem involves several mathematical concepts, including:

  • Percentages: We expressed the percentage as a decimal and used it to set up the equation.
  • Decimals: We converted the percentage to a decimal and used it to solve the equation.
  • Equations: We set up and solved an equation to find the cost of the procedure.
  • Variables: We isolated the variable and solved for it.

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

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

  • Read the problem carefully: Make sure you understand what the problem is asking for.
  • Express percentages as decimals: This will make it easier to set up and solve the equation.
  • Use a calculator: If you are having trouble solving the equation manually, use a calculator to help you.
  • Check your work: Make sure you have solved the equation correctly by checking your work.

Conclusion

In this article, we have answered some frequently asked questions about the problem and provided additional guidance on how to solve it. We have also highlighted the importance of understanding the problem, expressing percentages as decimals, and using a calculator to solve the equation. By following these tips and tricks, you can solve this problem and many others like it.