After The Bank Cashed A Check Maureen Wrote For \[$\$60\$\], Her Balance Was \[$-\$14\$\]. The Equation \[$b + (-60) = -14\$\] Can Be Used To Represent This Situation, Where \[$b\$\] Is Maureen's Balance, In Dollars,

Feb 28, 2025 by ADMIN 217 views

Solving Linear Equations: A Real-World Example

In this article, we will explore a real-world scenario that involves solving a linear equation. We will use the equation ${$ b + (-60) = -14$}$ to represent a situation where Maureen's bank balance changes after cashing a check. We will break down the equation, solve for the variable, and provide a step-by-step explanation of the process.

The equation ${$ b + (-60) = -14$}$ represents a situation where Maureen's bank balance, denoted by ${$ b$}$, changes after cashing a check for ${$ $60$}$. The equation can be read as: "Maureen's balance plus minus sixty dollars equals minus fourteen dollars." This equation is a linear equation, which means it can be represented in the form ${$ ax + b = c$}$, where ${$ a$}$, ${$ b$}$, and ${$ c$}$ are constants.

To solve the equation, we need to isolate the variable ${$ b$}$. We can start by combining the constants on the left-hand side of the equation. In this case, we have ${$ -60$}$ and ${$ -14$}$, which can be combined as follows:

${$ b + (-60) = -14$}{ $b - 60 = -14\$}$

Now that we have combined the constants, we can solve for the variable ${$ b$}$. To do this, we need to isolate ${$ b$}$ on one side of the equation. We can do this by adding ${ $60\$}$ to both sides of the equation:

${$ b - 60 = -14$}{ $b - 60 + 60 = -14 + 60\$}$ ${$ b = 46$}$

The solution to the equation, ${$ b = 46$}$, represents Maureen's bank balance after cashing the check. This means that Maureen's balance is ${$ $46$}$ after the check is cashed.

Solving linear equations is a fundamental concept in mathematics that has numerous real-world applications. In finance, linear equations are used to calculate interest rates, investment returns, and credit scores. In science, linear equations are used to model population growth, chemical reactions, and physical systems. In engineering, linear equations are used to design and optimize systems, such as bridges, buildings, and electronic circuits.

In this article, we have explored a real-world scenario that involves solving a linear equation. We have used the equation ${$ b + (-60) = -14$}$ to represent a situation where Maureen's bank balance changes after cashing a check. We have broken down the equation, solved for the variable, and provided a step-by-step explanation of the process. We have also discussed the real-world applications of solving linear equations and how it can be used to model and analyze various systems.

Here are a few additional examples of linear equations that can be used to model real-world scenarios:

Example 1: A bakery sells a total of ${$ $120$}$ worth of bread and pastries. If the bakery sells ${$ $60$}$ worth of bread and ${$ $20$}$ worth of pastries, how much does the bakery sell in total?
Example 2: A car travels a total of ${$ $200$}$ miles in ${$ $4$}$ hours. If the car travels ${$ $100$}$ miles in ${$ $2$}$ hours, how much does the car travel in total?
Example 3: A company has a total of ${$ $1000$}$ in assets. If the company has ${$ $500$}$ in cash and ${$ $300$}$ in inventory, how much does the company have in total?

These examples demonstrate how linear equations can be used to model and analyze various real-world scenarios.

Solving linear equations is a fundamental concept in mathematics that has numerous real-world applications. By understanding how to solve linear equations, we can model and analyze various systems, make informed decisions, and solve real-world problems. In this article, we have explored a real-world scenario that involves solving a linear equation and provided a step-by-step explanation of the process. We have also discussed the real-world applications of solving linear equations and how it can be used to model and analyze various systems.
Solving Linear Equations: A Real-World Example - Q&A

In our previous article, we explored a real-world scenario that involves solving a linear equation. We used the equation ${$ b + (-60) = -14$}$ to represent a situation where Maureen's bank balance changes after cashing a check. We broke down the equation, solved for the variable, and provided a step-by-step explanation of the process. In this article, we will answer some frequently asked questions about solving linear equations.

Q: What is a linear equation?

A: A linear equation is an equation that can be represented in the form ${$ ax + b = c$}$, where ${$ a$}$, ${$ b$}$, and ${$ c$}$ are constants.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the variable on one side of the equation. You can do this by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.

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

A: A linear equation is an equation that can be represented in the form ${$ ax + b = c$}$, where ${$ a$}$, ${$ b$}$, and ${$ c$}$ are constants. A quadratic equation is an equation that can be represented in the form ${$ ax^2 + bx + c = 0$}$, where ${$ a$}$, ${$ b$}$, and ${$ c$}$ are constants.

Q: How do I know if an equation is linear or quadratic?

A: To determine if an equation is linear or quadratic, you need to look at the highest power of the variable. If the highest power is 1, the equation is linear. If the highest power is 2, the equation is quadratic.

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

A: Yes, you can use a calculator to solve a linear equation. However, it's always a good idea to check your work by plugging the solution back into the original equation.

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

A: Solving linear equations has numerous real-world applications, including finance, science, and engineering. In finance, linear equations are used to calculate interest rates, investment returns, and credit scores. In science, linear equations are used to model population growth, chemical reactions, and physical systems. In engineering, linear equations are used to design and optimize systems, such as bridges, buildings, and electronic circuits.

Q: Can I use linear equations to solve systems of equations?

A: Yes, you can use linear equations to solve systems of equations. A system of equations is a set of two or more equations that are all true at the same time. You can use linear equations to solve systems of equations by using methods such as substitution or elimination.

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

A: Some common mistakes to avoid when solving linear equations include:

Not isolating the variable on one side of the equation
Not checking your work by plugging the solution back into the original equation
Not using the correct order of operations (PEMDAS)
Not simplifying the equation before solving it

Here are some additional resources for learning more about solving linear equations:

Online tutorials: There are many online tutorials and videos that can help you learn how to solve linear equations.
Practice problems: Practice problems are a great way to reinforce your understanding of solving linear equations.
Math textbooks: Math textbooks can provide a comprehensive overview of solving linear equations and other mathematical concepts.
Online communities: Online communities, such as math forums and social media groups, can provide a platform for asking questions and getting help with solving linear equations.

By using these resources and practicing regularly, you can become proficient in solving linear equations and apply this skill to real-world problems.