Problem 91 - Algebra A Combined Function

Question

Solve. See Example 22. During the PGA 2008 Wyndham Championship tournament, the winner, Carl Pettersson, had scores of \(-6,-9,-4,\) and \(-2 .\) What was his total score for the tournament? (Source: Professional Golfer's Association)

Step-by-Step Solution

Answer

Carl Pettersson's total score was -21.

Step 1: List the Scores

First, we need to understand what numbers we're working with. The scores for Carl Pettersson during the tournament are: - Round 1: \(-6\)- Round 2: \(-9\)- Round 3: \(-4\)- Round 4: \(-2\)

Step 2: Add the Scores

To find the total score, we need to add the scores from each round. This is calculated as follows:\(-6 + (-9) + (-4) + (-2)\)

Step 3: Simplify the Addition

Combine the scores step-by-step:- First, add \(-6\) and \(-9\):\(-6 + (-9) = -15\)- Next, add \(-4\) to \(-15\):\(-15 + (-4) = -19\)- Finally, add \(-2\) to \(-19\):\(-19 + (-2) = -21\)

Step 4: Interpret the Result

The total score for Carl Pettersson during the tournament is \(-21\). A negative score indicates strokes under par. Therefore, Carl Pettersson finished the tournament 21 strokes under par.

Key Concepts

Negative Numbers

Negative numbers are an essential part of math that represent values less than zero. They are used in various scenarios, from temperature readings below freezing to financial debts. In golf, negative scores are favorable, indicating strokes under par. Here’s how they interact with

• Sign: Negative numbers are denoted by a minus (-) sign. For instance, -3 indicates 3 units below zero.
• Interpretation: Each negative number in the context of the PGA Championship represents a round of strokes under par. A score of -9 means the player played nine strokes fewer than par in that round.
• Simple Comparison: Similar to positive numbers, negative numbers have an order; -1 is greater than -5.

Combining negative numbers in a sum brings us to a deeper understanding of addition, and how negative numbers act when you add them together.

Combining Like Terms

When adding integers, especially with negative numbers, combining like terms can simplify expressions. This principle is helpful across various problem types, not just golf scores. Here are the steps to combining like terms:

• Group Similar Numbers: Identify and group numbers with similar signs, like all negative numbers in one sum, to streamline addition.
• Perform Incremental Additions: Start adding the smallest numbers first to avoid mistakes during calculus. Begin with pairs if the list is long.
• Combine Sequentially: With the scores -6, -9, -4, and -2, the first step pairs -6 and -9 to be -15. Next, add -4 to make it -19 and end with -2 to finalize at -21.
• Check Consistency: After reaching the sum, back-calculate to ensure accuracy by summing parts again.

This stepwise approach helps students visualize the result clearer and mitigate errors in daily math tasks.

Integer Addition Problem-Solving Steps

Solving integer addition problems, especially with negative numbers, can be straightforward if we follow a structured approach. This process ensures clarity and accuracy.

• Identify Each Component: Begin by listing out each integer separately to avoid confusion, specifying which is negative or positive.
• Apply the Operations: Use parentheses for every negative number to ensure correct operation. Take it step-by-step from left to right as demonstrated in solving, -6 + (-9) + (-4) + (-2).
• Simplify Through Combination: Add the numbers in stages. First, -6 and -9 add up to -15. Then, add -4 resulting in -19, and finally approach with -2 to conclude at -21.
• Review the Problem: After computing the solution, consider the context, such as tournament rules, to understand meanings, like -21 signifying 21 strokes under par in golf, a positive feat.
• Reassure Through Recalculation: Revisiting parts can confirm the accuracy of the result.

Approaching problems through these steps nurtures stronger problem-solving skills.