Translate The Following Verbal Statement Into An Algebraic Equation And Then Solve:Kaden Paid $23,755 For A Car, Which Was $1,444 Less Than The Sticker Price. What Was The Sticker Price Of The Car?Use \[$ Z \$\] For Your
Understanding the Problem
Kaden, a car enthusiast, recently purchased a vehicle for $23,755. However, this amount is $1,444 less than the sticker price of the car. In this article, we will translate the verbal statement into an algebraic equation and then solve for the sticker price of the car.
Translating the Verbal Statement into an Algebraic Equation
To translate the verbal statement into an algebraic equation, we need to identify the variables and the relationships between them. Let's denote the sticker price of the car as x. The verbal statement can be broken down into two parts:
- Kaden paid $23,755 for the car.
- The sticker price is $1,444 more than the amount Kaden paid.
Using algebraic notation, we can represent the first part as:
23,755 = x - 1,444
Simplifying the Equation
To simplify the equation, we can add 1,444 to both sides of the equation:
23,755 + 1,444 = x
This simplifies to:
25,199 = x
Interpreting the Result
The result x = 25,199 represents the sticker price of the car. This means that the sticker price of the car is $25,199.
Checking the Solution
To verify the solution, we can substitute x = 25,199 back into the original equation:
23,755 = 25,199 - 1,444
Expanding the right-hand side of the equation, we get:
23,755 = 23,755
This confirms that the solution x = 25,199 is correct.
Conclusion
In this article, we translated the verbal statement into an algebraic equation and then solved for the sticker price of the car. The result x = 25,199 represents the sticker price of the car. This problem demonstrates the importance of algebraic notation in solving real-world problems.
Real-World Applications
This problem has real-world applications in various fields, such as finance, economics, and business. For example, in finance, understanding the sticker price of a car can help individuals make informed decisions about their investments. In economics, the sticker price of a car can be used to analyze the demand and supply of cars in the market. In business, understanding the sticker price of a car can help companies make informed decisions about their pricing strategies.
Tips and Tricks
When translating verbal statements into algebraic equations, it's essential to identify the variables and the relationships between them. In this problem, we used the variable x to represent the sticker price of the car. We also used the equation 23,755 = x - 1,444 to represent the relationship between the amount Kaden paid and the sticker price.
Common Mistakes
When solving algebraic equations, it's essential to avoid common mistakes such as:
- Not identifying the variables and the relationships between them.
- Not simplifying the equation correctly.
- Not verifying the solution.
By avoiding these common mistakes, individuals can ensure that their solutions are accurate and reliable.
Conclusion
In conclusion, this article demonstrated how to translate a verbal statement into an algebraic equation and then solve for the sticker price of a car. The result x = 25,199 represents the sticker price of the car. This problem has real-world applications in various fields, and individuals can use algebraic notation to solve similar problems.
Q: What is the first step in translating a verbal statement into an algebraic equation?
A: The first step in translating a verbal statement into an algebraic equation is to identify the variables and the relationships between them. This involves breaking down the verbal statement into smaller parts and representing each part using algebraic notation.
Q: How do I represent variables in an algebraic equation?
A: Variables are represented using letters, such as x, y, or z. In the problem we solved earlier, we used the variable x to represent the sticker price of the car.
Q: What is the difference between a verbal statement and an algebraic equation?
A: A verbal statement is a statement that is expressed in words, while an algebraic equation is a statement that is expressed using algebraic notation. For example, the verbal statement "Kaden paid $23,755 for a car" can be translated into the algebraic equation 23,755 = x - 1,444.
Q: How do I simplify an algebraic equation?
A: To simplify an algebraic equation, you can add or subtract the same value to both sides of the equation. For example, in the equation 23,755 = x - 1,444, we can add 1,444 to both sides to get 25,199 = x.
Q: What is the importance of verifying a solution?
A: Verifying a solution is essential to ensure that the solution is accurate and reliable. In the problem we solved earlier, we verified the solution by substituting x = 25,199 back into the original equation.
Q: How do I identify the relationships between variables in an algebraic equation?
A: To identify the relationships between variables in an algebraic equation, you need to analyze the equation and identify the operations that are being performed on the variables. For example, in the equation 23,755 = x - 1,444, we can see that x is being subtracted by 1,444.
Q: What are some common mistakes to avoid when translating verbal statements into algebraic equations?
A: Some common mistakes to avoid when translating verbal statements into algebraic equations include:
- Not identifying the variables and the relationships between them.
- Not simplifying the equation correctly.
- Not verifying the solution.
Q: How do I apply algebraic notation to real-world problems?
A: Algebraic notation can be applied to real-world problems by identifying the variables and the relationships between them. For example, in the problem we solved earlier, we used algebraic notation to represent the sticker price of a car and the amount Kaden paid.
Q: What are some real-world applications of algebraic notation?
A: Algebraic notation has many real-world applications, including finance, economics, and business. For example, in finance, algebraic notation can be used to analyze the demand and supply of stocks and bonds. In economics, algebraic notation can be used to model the behavior of economic systems. In business, algebraic notation can be used to analyze the pricing strategies of companies.
Q: How do I practice translating verbal statements into algebraic equations?
A: To practice translating verbal statements into algebraic equations, you can try solving problems that involve translating verbal statements into algebraic equations. You can also try creating your own problems and solving them using algebraic notation.
Q: What are some resources available for learning algebraic notation?
A: There are many resources available for learning algebraic notation, including textbooks, online tutorials, and practice problems. Some popular resources include Khan Academy, Mathway, and Wolfram Alpha.
Conclusion
In conclusion, this article provided answers to frequently asked questions about translating verbal statements into algebraic equations. We covered topics such as identifying variables and relationships, simplifying equations, and verifying solutions. We also discussed real-world applications of algebraic notation and provided resources for learning algebraic notation.