Jen Has A Newer Car Than Amelie, And It Has 1 3 \frac{1}{3} 3 1 ​ The Miles Of Amelie's Car. Amelie's Car Has 45,000 Miles. Which Of The Following Equations Model This Situation? Select All That Apply.A. 3 M = 45 , 000 3m = 45,000 3 M = 45 , 000 B. $\frac{1}{3} + M =

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Introduction

In real-world scenarios, mathematical equations are used to model and describe various situations. These equations help us understand complex relationships between different variables and make informed decisions. In this article, we will explore how to model a real-world situation involving two cars with different mileage.

The Problem

Jen has a newer car than Amelie, and it has 13\frac{1}{3} the miles of Amelie's car. Amelie's car has 45,000 miles. We need to determine which of the given equations model this situation.

Understanding the Situation

Let's break down the information provided:

  • Jen's car has 13\frac{1}{3} the miles of Amelie's car.
  • Amelie's car has 45,000 miles.

We can use this information to set up an equation that represents the relationship between the two cars.

Equation A: 3m=45,0003m = 45,000

Equation A states that three times the miles of Jen's car (3m3m) is equal to 45,000 miles. This equation is based on the fact that Jen's car has 13\frac{1}{3} the miles of Amelie's car. To find the miles of Jen's car, we can divide both sides of the equation by 3:

3m3=45,0003\frac{3m}{3} = \frac{45,000}{3}

Simplifying the equation, we get:

m=15,000m = 15,000

This means that Jen's car has 15,000 miles.

Equation B: 13+m=45,000\frac{1}{3} + m = 45,000

Equation B states that one-third plus the miles of Jen's car (13+m\frac{1}{3} + m) is equal to 45,000 miles. This equation is based on the fact that Jen's car has 13\frac{1}{3} the miles of Amelie's car. To find the miles of Jen's car, we can subtract 13\frac{1}{3} from both sides of the equation:

m=45,000−13m = 45,000 - \frac{1}{3}

Simplifying the equation, we get:

m=45,000−15,000m = 45,000 - 15,000

m=30,000m = 30,000

This means that Jen's car has 30,000 miles.

Conclusion

Based on the information provided, we can conclude that both Equation A and Equation B model the situation. However, Equation A is a more accurate representation of the relationship between the two cars.

Key Takeaways

  • Mathematical equations can be used to model real-world situations.
  • The equation 3m=45,0003m = 45,000 accurately represents the relationship between the two cars.
  • The equation 13+m=45,000\frac{1}{3} + m = 45,000 also models the situation, but it is not as accurate as Equation A.

Final Answer

The final answer is:

  • Equation A: 3m=45,0003m = 45,000
  • Equation B: 13+m=45,000\frac{1}{3} + m = 45,000

Q: What is the relationship between Jen's car and Amelie's car?

A: Jen's car has 13\frac{1}{3} the miles of Amelie's car.

Q: How many miles does Amelie's car have?

A: Amelie's car has 45,000 miles.

Q: What is the equation that represents the relationship between the two cars?

A: The equation 3m=45,0003m = 45,000 accurately represents the relationship between the two cars.

Q: Why is Equation A a more accurate representation of the relationship between the two cars?

A: Equation A is a more accurate representation of the relationship between the two cars because it directly states that three times the miles of Jen's car is equal to 45,000 miles.

Q: Can we use Equation B to find the miles of Jen's car?

A: Yes, we can use Equation B to find the miles of Jen's car. However, it is not as accurate as Equation A.

Q: What is the value of m in Equation B?

A: The value of m in Equation B is 30,000.

Q: Why is it important to understand the relationship between variables in a mathematical equation?

A: Understanding the relationship between variables in a mathematical equation is crucial in real-world applications. It helps us make informed decisions and solve complex problems.

Q: Can you provide an example of a real-world scenario where mathematical equations are used to model a situation?

A: Yes, here's an example:

Suppose a company wants to determine the cost of producing a certain number of units of a product. The cost of production is directly proportional to the number of units produced. In this scenario, a mathematical equation can be used to model the relationship between the number of units produced and the cost of production.

Q: How can we use mathematical equations to solve real-world problems?

A: We can use mathematical equations to solve real-world problems by:

  • Identifying the variables involved in the problem
  • Setting up an equation that represents the relationship between the variables
  • Solving the equation to find the value of the variables
  • Interpreting the results in the context of the problem

Q: What are some common applications of mathematical equations in real-world scenarios?

A: Some common applications of mathematical equations in real-world scenarios include:

  • Finance: mathematical equations are used to model stock prices, interest rates, and investment returns.
  • Engineering: mathematical equations are used to design and optimize systems, such as bridges, buildings, and electronic circuits.
  • Science: mathematical equations are used to model physical phenomena, such as the motion of objects, the behavior of particles, and the properties of materials.

Q: Can you provide some tips for solving mathematical equations in real-world scenarios?

A: Yes, here are some tips:

  • Read the problem carefully and identify the variables involved.
  • Set up an equation that represents the relationship between the variables.
  • Solve the equation using algebraic techniques, such as substitution and elimination.
  • Interpret the results in the context of the problem.
  • Check your work by plugging the solution back into the original equation.