Jade Has $ 451.89 \$451.89 $451.89 In Her Checking Account. After 3 Checks, Each For The Same Amount, Are Deducted From Her Account, She Has $ 358.92 \$358.92 $358.92 Left In Her Account.Assume She Makes No Other Withdrawals Or Deposits. Which Equations Represent

Introduction

In this article, we will delve into the world of mathematics and explore the concept of linear equations. We will use a real-life scenario to demonstrate how linear equations can be used to model and solve problems. Our scenario involves Jade, who has a checking account with an initial balance of $\$451.89$. After writing three checks, each for the same amount, she is left with $\$358.92$ in her account. We will use this information to create and solve linear equations that represent the situation.

The Problem

Let's break down the problem and identify the key elements:

• Jade starts with $\$451.89$ in her checking account.
• She writes three checks, each for the same amount.
• After writing the checks, she is left with $\$358.92$ in her account.

We can represent the amount of each check as a variable, say $x$. Since Jade writes three checks, the total amount deducted from her account is $3x$. We can set up an equation to represent the situation:

Equation 1: Total Amount Deducted

$$451.89 - 3x = 358.92$$

This equation represents the initial balance in Jade's account minus the total amount deducted from her account, which is equal to the final balance.

Solving the Equation

To solve for $x$, we can add $3x$ to both sides of the equation:

$$451.89 = 358.92 + 3x$$

Subtracting $358.92$ from both sides gives us:

$$93.97 = 3x$$

Dividing both sides by $3$ gives us:

$$x = 31.32$$

So, each check is for $\$31.32$.

Alternative Equation

We can also represent the situation using an alternative equation. Let's say the amount of each check is $x$. Then, the total amount deducted from Jade's account is $3x$. We can set up an equation to represent the situation:

Equation 2: Total Amount Deducted (Alternative)

$$451.89 - x = 358.92$$

This equation represents the initial balance in Jade's account minus the amount of each check, which is equal to the final balance.

Solving the Alternative Equation

To solve for $x$, we can add $x$ to both sides of the equation:

$$451.89 = 358.92 + x$$

Subtracting $358.92$ from both sides gives us:

$$92.97 = x$$

However, this solution is not consistent with the original problem, as it implies that each check is for $\$92.97$, which is not the case.

Conclusion

In this article, we used a real-life scenario to demonstrate how linear equations can be used to model and solve problems. We created and solved two equations that represent the situation: one using the total amount deducted from Jade's account, and another using the amount of each check. We found that the first equation yields a consistent solution, while the second equation does not. This highlights the importance of carefully setting up and solving equations to ensure that they accurately represent the problem at hand.

Key Takeaways

• Linear equations can be used to model and solve problems in a variety of contexts.
• Carefully setting up and solving equations is crucial to ensure that they accurately represent the problem at hand.
• Consistent solutions are essential to ensure that the equation accurately represents the situation.

Further Reading

For more information on linear equations and how they can be used to model and solve problems, see the following resources:

• Linear Equations
• Systems of Linear Equations
• Mathematics for Real-World Problems

References

• Mathematics for Real-World Problems
• Linear Equations
• Systems of Linear Equations
  Jade's Checking Account: A Mathematical Analysis - Q&A =====================================================

Introduction

In our previous article, we explored the concept of linear equations using a real-life scenario involving Jade's checking account. We created and solved two equations that represent the situation: one using the total amount deducted from Jade's account, and another using the amount of each check. In this article, we will answer some frequently asked questions (FAQs) related to the topic.

Q&A

Q: What is the initial balance in Jade's checking account?

A: The initial balance in Jade's checking account is $\$451.89$.

Q: How many checks did Jade write?

A: Jade wrote three checks.

Q: What is the amount of each check?

A: The amount of each check is $\$31.32$.

Q: How much money is left in Jade's account after writing the checks?

A: After writing the checks, Jade is left with $\$358.92$ in her account.

Q: Can you explain the concept of linear equations in simple terms?

A: A linear equation is an equation in which the highest power of the variable(s) is 1. In other words, it is an equation that can be written in the form $ax + b = c$, where $a$, $b$, and $c$ are constants, and $x$ is the variable.

Q: How do you solve a linear equation?

A: To solve a linear equation, you can use the following steps:

1. Add or subtract the same value to both sides of the equation to isolate the variable.
2. Multiply or divide both sides of the equation by the same value to solve for the variable.

Q: What is the difference between Equation 1 and Equation 2?

A: Equation 1 represents the total amount deducted from Jade's account, while Equation 2 represents the amount of each check. Equation 1 is a more accurate representation of the situation, as it takes into account the total amount deducted from Jade's account.

Q: Can you provide more examples of linear equations?

A: Here are a few more examples of linear equations:

• $2x + 5 = 11$
• $x - 3 = 7$
• $4x = 24$

Q: How do you determine if an equation is linear or not?

A: To determine if an equation is linear or not, you can check if the highest power of the variable(s) is 1. If it is, then the equation is linear. If not, then the equation is not linear.

Q: Can you explain the concept of systems of linear equations?

A: A system of linear equations is a set of two or more linear equations that are solved simultaneously. In other words, it is a set of equations that are related to each other and must be solved together.

Q: How do you solve a system of linear equations?

A: To solve a system of linear equations, you can use the following methods:

1. Substitution method: Substitute the expression for one variable from one equation into the other equation.
2. Elimination method: Add or subtract the same value to both sides of the equations to eliminate one variable.
3. Graphing method: Graph the equations on a coordinate plane and find the point of intersection.

Conclusion

In this article, we answered some frequently asked questions related to the topic of linear equations and Jade's checking account. We hope that this article has provided you with a better understanding of the concept of linear equations and how they can be used to model and solve problems.

Key Takeaways

• Linear equations can be used to model and solve problems in a variety of contexts.
• Carefully setting up and solving equations is crucial to ensure that they accurately represent the problem at hand.
• Consistent solutions are essential to ensure that the equation accurately represents the situation.

Further Reading

For more information on linear equations and how they can be used to model and solve problems, see the following resources:

• Linear Equations
• Systems of Linear Equations
• Mathematics for Real-World Problems

References

• Mathematics for Real-World Problems
• Linear Equations
• Systems of Linear Equations