Problem 7 - Algebra 1: Concepts and Skills

Question

GOLF In Exercises 6 and 7, use the table showing scores for two rounds of golf. $$ \begin{array}{|c|c|c|c|c|} \hline & {\text { Player } 1} & {\text { Player 2}} & {\text { Player 3 }} & {\text { Player 4 }} \\ \hline \text { Round 1} & {90} & {88} & {79} & {78} \\ \hline \text { Round 2} & {94} & {84} & {83} & {80} \\ \hline \end{array} $$ Which player has the lowest average? Which one has the highest average?

Step-by-Step Solution

Answer

The player with the lowest average score is Player 4 with a score of 79. The player with the highest average score is Player 1 with a score of 92.

Step 1: Calculate the average for each player

The average score for a player over two rounds can be calculated by adding the scores of round 1 and round 2 together, then dividing the result by 2. Let's do this for each player. Use the table to gather the data: For Player 1, the average is \(\frac{90+94}{2}=92\), for Player 2 it's \(\frac{88+84}{2}=86\), for Player 3 it's \(\frac{79+83}{2}=81\), and for Player 4 it's \(\frac{78+80}{2}=79\).

Step 2: Identify the player with the lowest average

Looking at the calculated averages, we see that Player 4 has the lowest average score, with a score of 79.

Step 3: Identify the player with the highest average

Comparing the calculated averages again, we find that Player 1 has the highest average score, with a score of 92

Key Concepts

Data Interpretation

When dealing with problems related to data interpretation, it is crucial to understand how data is presented and how to extract relevant information from it. Consider the table illustrating the golf scores of four players over two rounds. Each cell represents a player's score in a specific round. To interpret this data effectively:

• Identify each player's performance in the individual rounds by examining the corresponding cells.
• Recognize that each row after 'Round 1' and 'Round 2' contains scores you need to use for calculations. Columns segregate the data pertaining to each player.
• Understand the objective of the problem, which is to determine who has the lowest and highest average scores based on the provided data.

This foundational step is about understanding what each number represents and making sense of the relationships between these numbers to solve the problem efficiently.

Arithmetic Operations

Arithmetic operations are fundamental to calculating and interpreting mathematical problems. In this context, average score calculation involves basic operations like addition and division:

• Addition: Sum the scores of the two rounds for each player. For example, Player 1's scores are added to produce a total score of 90 + 94 = 184.
• Division: Divide the total score by the number of rounds to find the average. In the case of Player 1, you divide 184 by 2, resulting in an average score of 92.

Understanding these operations ensures you can compute averages correctly, which is vital in finding solutions to such problems. Repetition of this process across different datasets reaffirms understanding of arithmetic calculations.

Problem-Solving in Mathematics

Approaching mathematical problems like identifying the lowest and highest averages requires a solid problem-solving strategy. Here's a step-by-step breakdown:

• Collect and Organize Data: Begin by extracting scores from the table and preparing to perform calculations for each player.
• Calculate Averages: Use arithmetic operations, as detailed earlier, to determine the average scores of each player.
• Comparison: Once averages are computed, compare these scores to determine the lowest and highest averages. For instance, identify that Player 4, with an average of 79, has the lowest score, while Player 1, with an average of 92, boasts the highest score.
• Conclude: Present your findings clearly, emphasizing who performed best and worst on average.

This approach not only aids in solving similar mathematical problems but also enhances analytical thinking skills essential in interpreting and analyzing mathematical data efficiently.