Problem 116 - Prealgebra and Introductory Algebra

Question

The combined scores of the top five golfers in a tournament equaled \(-10\) (10 under par). What was the average score of the five golfers? (THE IMAGES CANNOT COPY)

Step-by-Step Solution

Answer

The average score of the five golfers is -2.

Step 1: Analyze the Problem Structure

In this problem, the total score of the five golfers is given to be -10. This score has to be divided among five golfers equally since we are looking for the average score.

Step 2: Compute the Average

The average score is calculated by dividing the total score by the number of players. Using this formula, the average score would be \(-\frac{10}{5}\)

Step 3: Simplify the Calculation

Simplification gives us -2 which is the average score of the top five golfers.

Key Concepts

Understanding Negative Numbers

Negative numbers are simply numbers that are less than zero. They are represented with a minus sign (-) in front of them. In the context of golf, negative scores are actually good because they indicate the number of strokes below par a golfer has taken.
For example, if a golfer scores -10, it means the player took 10 fewer strokes than the par for the course, which is excellent in the game of golf.
Understanding negative numbers is essential as they often appear in different scenarios like in debts or temperatures below zero.

The Importance of Division in Calculating Averages

Division is a mathematical operation that involves splitting a number into equal parts. It is crucial in finding averages, where we evenly distribute a total sum among the number of parts we have.
In our assignment, to find the average score of the golfers, you divide the total score by the number of golfers.
So, if the total combined score is -10 and there are 5 golfers, you perform the division \( -\frac{10}{5} \) which equals -2. This result means, on average, each golfer scored 2 strokes below par.

Tournament Scoring

In many sports, scoring can determine the winner or the rank of participants. In golf tournaments, scores below par are desired, and negative scores showcase better performance.

• Par is the pre-determined number of strokes that an expert golfer should require to complete a hole or course.
• When a golfer scores under par, it implies efficiently playing the game with fewer strokes.
• Conversely, scores over par indicate more strokes and less efficiency.

Thus, a score of -10 collectively for golfers signifies an outstanding level of play collectively.

Applying Problem Solving Techniques

Problem solving refers to understanding an issue and finding an appropriate way to resolve it. In math exercises like this, breaking down the problem is key.
First, identify what you are given and what is required. For this problem, you know the total score and the number of participants; you need to find the average score.
Next, use the appropriate mathematical method, such as division in this context, and ensure each step logically leads to the solution.
Also, understanding the context like the scoring norms can guide you toward correctly interpreting results.