Wayne Stopped To Get Gas Before Going On A Road Trip. The Tank Already Had 4 Gallons Of Gas In It. Which Equation Relates The Total Amount Of Gasoline In The Tank, Y Y Y , To The Number Of Gallons That She Put In The Tank, X X X ?A. $y

When embarking on a road trip, it's essential to have a full tank of gas to ensure a safe and enjoyable journey. In this scenario, Wayne has already filled his tank with 4 gallons of gas before adding more. The question arises: how can we relate the total amount of gasoline in the tank, denoted as $y$, to the number of gallons that Wayne put in the tank, represented as $x$?

The Concept of Linear Equations

To solve this problem, we need to understand the concept of linear equations. A linear equation is a mathematical expression that represents a straight line on a graph. It is typically written in the form of $y = mx + b$, where $m$ is the slope of the line and $b$ is the y-intercept.

The Equation of the Total Amount of Gasoline

In this case, the total amount of gasoline in the tank, $y$, is directly related to the number of gallons that Wayne put in the tank, $x$. Since the tank already had 4 gallons of gas, we can represent this as the initial value of $y$. When Wayne adds more gas, the total amount of gasoline in the tank increases by the amount he puts in.

The Correct Equation

The correct equation that relates the total amount of gasoline in the tank, $y$, to the number of gallons that Wayne put in the tank, $x$, is:

$$y = 4 + x$$

This equation states that the total amount of gasoline in the tank, $y$, is equal to the initial amount of 4 gallons plus the number of gallons that Wayne put in, $x$.

Why This Equation is Correct

This equation is correct because it takes into account the initial amount of gasoline in the tank and the additional amount that Wayne put in. By adding the two values together, we get the total amount of gasoline in the tank.

Alternative Equations

Some alternative equations that may seem plausible at first glance are:

• $y = x + 4$
• $y = 4x$
• $y = 4 + 2x$

However, these equations are not correct because they do not accurately represent the relationship between the total amount of gasoline in the tank and the number of gallons that Wayne put in.

Conclusion

In conclusion, the correct equation that relates the total amount of gasoline in the tank, $y$, to the number of gallons that Wayne put in the tank, $x$, is:

$$y = 4 + x$$

This equation accurately represents the relationship between the two variables and is a fundamental concept in mathematics.

Additional Examples

Here are a few more examples of linear equations that relate to real-world scenarios:

• A bakery sells a total of 250 loaves of bread per day. If they sell 50 loaves in the morning and 100 loaves in the afternoon, how many loaves do they sell in the evening?

  $$y = 250 - 50 - 100$$

  $$y = 100$$

• A car travels a total distance of 200 miles. If it travels 50 miles in the first hour and 75 miles in the second hour, how many miles does it travel in the third hour?

  $$y = 200 - 50 - 75$$

  $$y = 75$$

Real-World Applications

Linear equations have numerous real-world applications, including:

• Finance: Linear equations can be used to calculate interest rates, investment returns, and loan payments.
• Science: Linear equations can be used to model population growth, chemical reactions, and physical systems.
• Engineering: Linear equations can be used to design and optimize systems, such as bridges, buildings, and electronic circuits.

Tips and Tricks

Here are a few tips and tricks for working with linear equations:

• Simplify the equation: Before solving the equation, try to simplify it by combining like terms.
• Use algebraic manipulation: Use algebraic manipulation to isolate the variable and solve for its value.
• Check your work: Always check your work by plugging the solution back into the original equation.

In our previous article, we explored the concept of linear equations and how they can be used to relate the total amount of gasoline in a tank to the number of gallons that were put in. We also discussed the importance of linear equations in various real-world applications, including finance, science, and engineering.

In this article, we will answer some frequently asked questions about linear equations and provide additional examples of their real-world applications.

Q: What is a linear equation?

A linear equation is a mathematical expression that represents a straight line on a graph. It is typically written in the form of $y = mx + b$, where $m$ is the slope of the line and $b$ is the y-intercept.

Q: How do I solve a linear equation?

To solve a linear equation, you need to isolate the variable by using algebraic manipulation. This involves adding, subtracting, multiplying, or dividing both sides of the equation by the same value to get the variable by itself.

Q: What is the difference between a linear equation and a quadratic equation?

A linear equation is a mathematical expression that represents a straight line on a graph, while a quadratic equation is a mathematical expression that represents a parabola on a graph. Quadratic equations are typically written in the form of $y = ax^2 + bx + c$, where $a$, $b$, and $c$ are constants.

Q: Can linear equations be used to model real-world scenarios?

Yes, linear equations can be used to model real-world scenarios, such as population growth, chemical reactions, and physical systems. They can also be used to calculate interest rates, investment returns, and loan payments.

Q: What are some real-world applications of linear equations?

Some real-world applications of linear equations include:

• Finance: Linear equations can be used to calculate interest rates, investment returns, and loan payments.
• Science: Linear equations can be used to model population growth, chemical reactions, and physical systems.
• Engineering: Linear equations can be used to design and optimize systems, such as bridges, buildings, and electronic circuits.

Q: How can I use linear equations to solve problems in real-world scenarios?

To use linear equations to solve problems in real-world scenarios, you need to:

1. Identify the variables and constants in the problem.
2. Write a linear equation that represents the relationship between the variables.
3. Solve the equation using algebraic manipulation.
4. Check your work by plugging the solution back into the original equation.

Q: What are some common mistakes to avoid when working with linear equations?

Some common mistakes to avoid when working with linear equations include:

• Not simplifying the equation: Before solving the equation, try to simplify it by combining like terms.
• Not using algebraic manipulation: Use algebraic manipulation to isolate the variable and solve for its value.
• Not checking your work: Always check your work by plugging the solution back into the original equation.

Q: How can I practice working with linear equations?

To practice working with linear equations, you can:

• Solve problems: Practice solving problems that involve linear equations.
• Use online resources: Use online resources, such as Khan Academy and Mathway, to practice working with linear equations.
• Work with a tutor: Work with a tutor to practice working with linear equations.

By following these tips and practicing working with linear equations, you can become proficient in using them to solve problems in real-world scenarios.

Additional Examples

Here are a few more examples of linear equations and their real-world applications:

• A company sells a total of 1000 units of a product per day. If they sell 200 units in the morning and 300 units in the afternoon, how many units do they sell in the evening?

  $$y = 1000 - 200 - 300$$

  $$y = 500$$

• A car travels a total distance of 300 miles. If it travels 50 miles in the first hour and 75 miles in the second hour, how many miles does it travel in the third hour?

  $$y = 300 - 50 - 75$$

  $$y = 175$$

Real-World Applications

Linear equations have numerous real-world applications, including:

• Finance: Linear equations can be used to calculate interest rates, investment returns, and loan payments.
• Science: Linear equations can be used to model population growth, chemical reactions, and physical systems.
• Engineering: Linear equations can be used to design and optimize systems, such as bridges, buildings, and electronic circuits.

By understanding linear equations and their real-world applications, you can become proficient in using them to solve problems in various fields.