Problem 63 - Algebra 1: Concepts and Skills

Question

For a correct answer on a game show, a positive amount is added to a player's score. For an incorrect answer, a negative amount is added. If a player has a score of \(-100\) and incorrectly answers a 300 point question, what is the player's new score? F. \(-400\) G. \(-200\) C. 200 D. 400

Step-by-Step Solution

Answer

F. -400

Step 1: Identify the Initial Score

The player's starting score is -100 points.

Step 2: Understand the Addition for Incorrect Answer

An incorrectly answered question implies that 300 points are subtracted from the score. So we effectively have to subtract 300 from -100.

Step 3: Find the New Score

The new score is found by the following operation: \(-100 - 300 = -400\).

Key Concepts

Addition and Subtraction of Integers

When we work with integers, it's important to understand how adding and subtracting them can change the value depending on whether the number is positive or negative.

For addition:

• When you add two positive numbers, the result is positive because you're increasing the value.
• When you add two negative numbers, the result is negative, which means you're making the total value more negative. Essentially, you're adding the deficiency.
• Adding a positive and negative number requires comparing their absolute values, and the sign of the result depends on which had the larger absolute value.

For subtraction:

• Subtracting a positive number is like adding a negative. It brings the value down.
• Subtracting a negative number is the same as adding its positive counterpart. It increases the value.

The difference between subtraction and addition with integers is mostly intuitive. Observing the change in signs helps identify how these operations affect the overall value.

Negative Numbers

Understanding negative numbers is crucial, especially when dealing with scores. Negative numbers represent values less than zero and can be thought of as being in debt.

When you work with negative numbers:

• If you add a positive number to a negative number, you move toward zero, reducing the negative value.
• Adding two negative numbers results in a more negative outcome, just as adding weights increases the heaviness.
• Subtracting a negative number can make it more positive because it's equivalent to adding a positive number.

Consider temperatures: if it's egin{equation} -10°C ext{ and you gain heat , you might end up at } 0°C ext{ or beyond .} ext{ If it turns cooler by } 5°, it turns into } -15°C ext{ because you added cold .} ext{ Mastering them is truly essential for, say, calculation of person 's finances } or game scores.

Score Calculation

In contexts like game shows, calculating a score requires you to adjust according to right or wrong answers, represented by positive and negative numbers, respectively.

To determine a player's new score after a guess:

• Start with the initial score, which could be positive or negative.
• For a correct answer, typically a positive point value is added, increasing the score.
• For an incorrect answer, a negative point value is included, which decreases the overall score. Essentially, you're performing a subtraction operation on the score.

Let's break it down for the problem at hand: The player's initial score is -100 . If they answer a 300-point question incorrectly, consider this as an addition of -300 points. The calculation becomes -100 - 300 = -400 . This score calculation shows how important it is to carefully work with integers, ensuring you apply the right operation signs to reach an accurate score.