Problem 63 - Beginning and Intermediate Algebra

Question

In golf, scores that are under par for the entire round are shown as negative scores; positive scores are shown for scores that are over par, and 0 is par. Paula Creamer was the winner of the 2007 LPGA SBS Open at Turtle Bay. Her scores were \(-5,-2,\) and \(-2 .\) What was her overall score? (Source: Ladies Professional Golf Association)

Step-by-Step Solution

Answer

Paula's overall score was \(-9\).

Step 1: Understand Paula's Scores

Paula's scores for each of the rounds are given as \(-5\), \(-2\), and \(-2\). This means she scored \(-5\) under par for the first round, \(-2\) under par for the second round, and \(-2\) under par for the third round.

Step 2: Sum the Negative Scores

To find Paula's overall score for the tournament, we need to sum the scores from all three rounds: \(-5 + (-2) + (-2)\).

Step 3: Calculate the Total Score

Perform the addition: First, sum the scores of the last two rounds: \(-2 + (-2) = -4\). Now, add it to the first round score: \(-5 + (-4) = -9\).

Step 4: Interpret the Result

The sum of \(-5\), \(-2\), and \(-2\) gives Paula a total score of \(-9\). This means Paula finished 9 strokes under par for the entire tournament.

Key Concepts

Negative Numbers

In mathematics, negative numbers are values less than zero, represented with a minus sign (\(-\)) in front of them. Understanding negative numbers is essential because they frequently occur in various real-world contexts, such as golf scores or temperatures below freezing.

Negative numbers are used to indicate a direction opposite to positive numbers — they are not just smaller than zero, but also represent a deficit or a reduction. Consider when someone mentions being 10 degrees below zero; this would be expressed as \(-10\) degrees.

When working with negative numbers, it is crucial to remember:

• Every negative number is less than zero and every positive number.
• Negative numbers are the result of subtracting a greater number from a smaller number.

Mathematical Operations

Mathematical operations involving negative numbers can initially seem counterintuitive, but they follow logical rules. When adding negative numbers, you effectively decrease the number you're adding to.

For example, if Paula's golf scores vary from \(-5\), \(-2\), and \(-2\), adding these together requires simple steps:

Combine \(-2 + (-2)\) first. Negative numbers add together just like positive numbers, but keep their sign: \(-2 + (-2) = -4\). Then, add this result to \(-5\):

• \(-5 + (-4) = -9\)

This total illustrates how negative numbers can reflect performance, with each addition of a negative further reducing the total count or metric, such as a score.

If encountering difficulty, visualize it as moving backwards on a number line, each negative addition taking you further left beyond zero.

Real-life Math Applications

Using math to solve real-life problems makes concepts more relatable and beneficial. In sports, like golf, scores are often interpreted using negative numbers. These numbers provide important information about performance relative to a standard (par).

Athletes like Paula Creamer in our example, achieve scores like \(-9\) by consistently playing under par across multiple rounds.

This practical application of math underscores a few important points:

• It demonstrates tracking progress and measuring success through mathematical calculations.
• It highlights improved performance, as lower scores (more negative) represent better outcomes in golf.

Whether calculating a budget or understanding temperature changes, negative numbers and their operations are fundamental in assessing and interpreting data meaningfully.