Solving The Mystery: Jade's Checking Account Equations

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Hey there, math enthusiasts! Let's dive into a real-world problem that many of us can relate to: managing our bank accounts. Today, we're helping Jade figure out how much each of her checks was worth. We'll use equations to crack the code and find the answer. So, grab your calculators (or your brains!) and let's get started. We'll explore how to translate a word problem into a mathematical equation. We'll be using algebra to solve for an unknown variable. And, we'll confirm the solution by checking the answer.

The Problem: Jade's Finances in Focus

So, here's the deal, guys. Jade has a certain amount of money in her checking account – a cool $451.89 to be exact. Then, she writes three checks, and each one is for the same amount. After those checks are cashed, her account balance drops to $358.92. The big question is: How much was each check worth? This is where our mathematical detective work begins.

We need to translate this word problem into a mathematical equation. To do this, we first need to identify the key pieces of information: the starting amount in the checking account, the number of checks written, the amount each check is worth (which is unknown), and the final balance in the checking account after the checks have been cashed. Jade began with a starting balance of $451.89. Then, she wrote three checks, each valued at some amount. After those three checks are deducted from her checking account, she has $358.92 remaining. This is enough information to craft the equation.

When working on math problems, especially word problems, it is important to carefully read and understand the problem. The first step to solving a word problem is understanding what the problem is asking. This will help you to identify the knowns and unknowns. In this case, the unknown is the amount each check is worth, and we need to determine the mathematical relationship between the known and unknown values. In this case, the knowns are Jade's starting balance and the final balance, as well as the number of checks written. Once we have determined the knowns and unknowns, we can create the equation.

To make things easier, we're going to use a variable to represent the unknown amount of each check. Let's use the letter 'c' to stand for the value of one check. Since Jade wrote three checks, the total amount deducted from her account will be 3 times the value of one check, or 3c. We know that the beginning balance ($451.89) minus the total value of the checks (3c) equals the final balance ($358.92). This gives us the equation $451.89 - 3c = $358.92.

Unveiling the Equations: Choosing the Right Formula

Okay, team, let's explore some equations that represent this situation. Remember, we are trying to determine which equation correctly describes the relationship between Jade's initial balance, the check amounts, and her final balance.

Here's how we can represent the problem mathematically:

  • Initial Balance - (3 x Check Amount) = Final Balance
  • $451.89 - 3c = $358.92

Where:

  • '$451.89' is Jade's starting balance.
  • 'c' is the amount of one check.
  • '3c' is the total amount deducted from her account (3 checks).
  • '$358.92' is Jade's final balance.

Therefore, the correct equation that represents the scenario is $451.89 - 3c = $358.92. This equation accurately reflects the situation: Jade's initial balance, minus the total value of the three checks, equals her remaining balance. Any other equation would not correctly represent the relationship between Jade's initial account balance, the checks written, and the remaining balance after the checks were cashed. Now we know which equation represents Jade's check value, we will solve the equation.

To solve for 'c' (the check amount), we need to isolate 'c'. The first step is to subtract $451.89 from both sides of the equation. This yields -3c = $358.92 - $451.89, or -3c = -$92.97. Next, we divide both sides by -3 to find c = $30.99. Therefore, each check was worth $30.99.

Solving for the Unknown: Finding the Check Amount

Alright, let's get down to business and actually solve for 'c', the value of each check. We will isolate the variable 'c' on one side of the equation and solve for its value. The equation we will solve is: $451.89 - 3c = $358.92.

To solve for 'c', we need to isolate it. Here's how we do it step-by-step:

  1. Subtract $451.89 from both sides:

    • $451.89 - 3c - $451.89 = $358.92 - $451.89
    • This simplifies to: -3c = -$92.97

  2. Divide both sides by -3:

    • -3c / -3 = -$92.97 / -3
    • This gives us: c = $30.99

So, after working the calculations, we find that c = $30.99. This means that each check Jade wrote was for $30.99. Now that we have calculated the amount of one check, we should check our answer to ensure it is accurate. The equation given was $451.89 - 3c = $358.92. Now that we know that each check, c, equals $30.99, we can substitute that value into the equation. So, $451.89 - 3($30.99) = $358.92.

Let's check our work: $451.89 - (3 * $30.99) = $451.89 - $92.97 = $358.92. Our final answer matches the final balance provided in the problem, and therefore our calculation is accurate.

Checking Your Work: Does the Answer Make Sense?

It's always a good idea to check your answer, guys. Math is all about accuracy, so let's make sure our answer makes sense and that we did the math right! Once we solve for 'c', we should plug the solution back into the equation to verify its accuracy. To check our answer, we can do the following calculation.

  1. Multiply the check amount by 3:

    • $30.99 x 3 = $92.97

  2. Subtract the total check amount from the initial balance:

    • $451.89 - $92.97 = $358.92

Our answer is correct! Subtracting the total value of the checks ($92.97) from Jade's starting balance ($451.89) gives us her final balance ($358.92). The final balance ($358.92) is the same value that was provided in the problem.

We correctly calculated the amount of one check. Now that we know the amount of one check, we can verify that our solution is correct. We can verify the solution by multiplying our solution for one check ($30.99) by three checks. Then we can deduct the product from Jade's starting balance to see if the resulting value matches the final balance provided in the question. And it does.

Conclusion: Equation Success!

Awesome work, everyone! We successfully deciphered the problem, identified the correct equation, and solved for the amount of each check. We also checked our work to ensure our solution was accurate. Remember, breaking down a word problem step by step, identifying the knowns and unknowns, and using the right equation is key to finding the solution. Keep practicing, and you'll become math wizards in no time!

This exercise highlights the practical application of algebra in everyday situations. By understanding how to translate real-world scenarios into equations, we can effectively solve various problems. This skill isn't just useful for academics; it's a valuable tool for personal finance, budgeting, and much more.

Now you're ready to tackle similar problems with confidence. Keep practicing, and you'll find that math, just like Jade's checking account, becomes much more manageable! Hopefully, this article helped you better understand how to identify and solve algebraic equations.