Problem 82 - Algebra A Combined Function

Question

In some card games, it is possible to have a negative score. Lavonne Schultz currently has a score of 15 points. She then loses 24 points. What is her new score?

Step-by-Step Solution

Answer

Lavonne's new score is -9.

Step 1: Understanding the Problem

Lavonne Schultz currently has a score of 15 points. We need to calculate her new score after she loses 24 points.

Step 2: Representing the Score Mathematically

Lavonne's current score is 15 points. If she loses 24 points, her new score can be represented by the equation: \( 15 - 24 \).

Step 3: Calculating the New Score

Calculate the new score by performing the subtraction: \( 15 - 24 = -9 \).

Step 4: Conclusion

Lavonne's new score after losing 24 points is \( -9 \).

Key Concepts

Understanding Negative Numbers

Negative numbers are often intimidating, but they are simply numbers that are less than zero. Think of them as representing values below a baseline, like temperature below freezing or scoring below zero in a game.
When you see a negative number, it's helpful to imagine things like:

• Debt (negative bank balance)
• A temperature drop (below zero degrees)
• Subtracting items instead of adding them

In games, if you score negatively, this means you've lost more points than you've gained. It can be seen like going down on an elevator past the ground floor into the basement. This means that when Lavonne's score changed to -9, she had gone into the negative score "territory," essentially showing a loss of 9 points overall.

Addition and Subtraction with Negative Numbers

Working with negative numbers in addition and subtraction is common in real life. The main trick is to know when to add or subtract.
When you subtract a bigger number from a smaller one, like in Lavonne's case where she has 15 and loses 24, you're essentially saying:

• Lose 15 to get to zero
• Then lose another 9 to account for the total 24

This results in a score of -9. It's like moving 9 steps below zero. So, the change is found by subtracting, which shifts the number line to the left of zero. Remember:

• Subtracting a negative is like adding (negative of a negative = positive)
• Keep the direction in mind; use smaller numbers as losses against larger ones

This simple method can help you easily visualize and compute similar problems.

Mathematical Representation of Scores

Representing scores mathematically allows us to easily compute and communicate numerical changes. Lavonne's score change was represented by the equation: 15 - 24.
This equation helps in:

• Showing the initial and final value of the score
• Illustrating the process from start to finish
• Offering a clear roadmap of how much change occurred

Such equations serve as a universal language to express shifts in values. When seeing or writing one, you typically start with the current number, apply the change to it (using subtraction in this case), and then show the result.
This approach not only simplifies calculations but also enhances understanding. By laying out the equation like a story, you reveal each part of the journey from start to finish and make the number shift clearer and more logical for anyone trying to understand the problem.