Ele's Car Is { X$}$ Years Old, And Kat's Car Is { Y$}$ Years Old. Kat's Car Is 3 Times As Old As Ele's Car. If Kat's Car Is Also 6 Years Older Than Ele's Car, Which Of The Following Systems Of Equations Best Models This
Introduction
In this article, we will explore a mathematical problem involving two cars, one belonging to Ele and the other to Kat. We will use algebraic equations to model the situation and determine which system of equations best represents the given information.
The Problem
Ele's car is {x$}$ years old, and Kat's car is {y$}$ years old. Kat's car is 3 times as old as Ele's car. If Kat's car is also 6 years older than Ele's car, which of the following systems of equations best models this situation?
Understanding the Problem
Let's break down the information given in the problem:
- Ele's car is {x$}$ years old.
- Kat's car is {y$}$ years old.
- Kat's car is 3 times as old as Ele's car, which can be represented as {y = 3x$}$.
- Kat's car is also 6 years older than Ele's car, which can be represented as {y = x + 6$}$.
Modeling the Situation
We have two pieces of information that can be represented as equations:
- {y = 3x$}$ (Kat's car is 3 times as old as Ele's car)
- {y = x + 6$}$ (Kat's car is 6 years older than Ele's car)
Systems of Equations
A system of equations is a set of two or more equations that are solved simultaneously to find the values of the variables. In this case, we have two equations:
- {y = 3x$}$
- {y = x + 6$}$
Equating the Equations
To find the values of {x$}$ and {y$}$, we can equate the two equations:
${3x = x + 6\$}
Solving for {x$}$
Subtracting {x$}$ from both sides of the equation gives us:
${2x = 6\$}
Dividing both sides of the equation by 2 gives us:
{x = 3$}$
Finding {y$}$
Now that we have the value of {x$}$, we can substitute it into one of the original equations to find the value of {y$}$. Let's use the equation {y = 3x$}$:
{y = 3(3)$] [y = 9\$}
Conclusion
The system of equations that best models the situation is:
{y = 3x$}{y = x + 6\$}
This system of equations represents the relationship between the ages of Ele's car and Kat's car, and can be used to find the values of {x$}$ and {y$}$.
Final Answer
The final answer is:
{y = 3x$}{y = x + 6\$}
This system of equations best models the situation described in the problem.
Introduction
In our previous article, we explored a mathematical problem involving two cars, one belonging to Ele and the other to Kat. We used algebraic equations to model the situation and determine which system of equations best represents the given information. In this article, we will answer some frequently asked questions related to the problem.
Q: What is the relationship between the ages of Ele's car and Kat's car?
A: The relationship between the ages of Ele's car and Kat's car is that Kat's car is 3 times as old as Ele's car, and Kat's car is also 6 years older than Ele's car.
Q: How can we represent the relationship between the ages of Ele's car and Kat's car using equations?
A: We can represent the relationship between the ages of Ele's car and Kat's car using the following equations:
{y = 3x$}$ (Kat's car is 3 times as old as Ele's car) {y = x + 6$}$ (Kat's car is 6 years older than Ele's car)
Q: How do we solve for the values of {x$}$ and {y$}$?
A: To solve for the values of {x$}$ and {y$}$, we can equate the two equations:
${3x = x + 6\$}
Subtracting {x$}$ from both sides of the equation gives us:
${2x = 6\$}
Dividing both sides of the equation by 2 gives us:
{x = 3$}$
Now that we have the value of {x$}$, we can substitute it into one of the original equations to find the value of {y$}$. Let's use the equation {y = 3x$}$:
{y = 3(3)$] [y = 9\$}
Q: What is the value of {x$}$ and {y$}$?
A: The value of {x$}$ is 3, and the value of {y$}$ is 9.
Q: Which system of equations best models the situation?
A: The system of equations that best models the situation is:
{y = 3x$}{y = x + 6\$}
Q: What is the significance of the system of equations?
A: The system of equations represents the relationship between the ages of Ele's car and Kat's car, and can be used to find the values of {x$}$ and {y$}$.
Q: Can we use the system of equations to solve other problems?
A: Yes, we can use the system of equations to solve other problems that involve relationships between variables.
Conclusion
In this article, we answered some frequently asked questions related to the problem of Ele's car and Kat's car. We hope that this article has provided a better understanding of the problem and the system of equations that best models the situation.
Final Answer
The final answer is:
{y = 3x$}{y = x + 6\$}
This system of equations best models the situation described in the problem.