Problem 97 - Intermediate Algebra

Question

Write a numerical statement to represent the problem. Then simplify the numerical expression to answer the question. Jeff played 18 holes of golf on Saturday. On each of 6 holes he was 1 under par, on each of 4 holes he was 2 over par, on 1 hole he was 3 over par, on each of 2 holes he shot par, and on each of 5 holes he was 1 over par. How did he finish relative to par?

Step-by-Step Solution

Answer

Jeff finished +10 relative to par.

Step 1: Interpret the Problem

First, we need to understand the numerical representation of Jeff's scores. Being 1 under par means scoring -1, 2 over par means scoring +2, 3 over par means scoring +3, par means scoring 0, and 1 over par means scoring +1.

Step 2: Set Up the Numerical Expression

Based on the problem information, we can set up the expression:- Jeff was 1 under par on 6 holes: 6(-1) - He was 2 over par on 4 holes: 4(+2)- He was 3 over par on 1 hole: 1(+3)- He shot par on 2 holes: 2(0)- He was 1 over par on 5 holes: 5(+1)The expression to evaluate is: \[ 6(-1) + 4(+2) + 1(+3) + 2(0) + 5(+1) \]

Step 3: Calculate the Components

Calculate each part of the expression separately:- \( 6(-1) = -6 \)- \( 4(+2) = 8 \)- \( 1(+3) = 3 \)- \( 2(0) = 0 \)- \( 5(+1) = 5 \)

Step 4: Combine the Results

Now add all the results from the calculations together:\[ -6 + 8 + 3 + 0 + 5 \]

Step 5: Simplify the Expression

Combine the numbers:\( -6 + 8 = 2 \)\( 2 + 3 = 5 \)\( 5 + 0 = 5 \)\( 5 + 5 = 10 \)

Step 6: Conclusion

Jeff finished the game +10 relative to par after completing all the calculations.

Key Concepts

Golf Scoring

Golf scoring can seem a bit daunting at first but is actually quite simple once you grasp the basics. In golf, each hole has an expected number of strokes known as "par." A golfer's score is measured by how many strokes they take in relation to par.

Here's the key:

• If a player completes a hole using fewer strokes than par, they are "under par." For example, if par is 4 and they score a 3, they are 1 under par (-1).
• Conversely, scoring more than par means the player is "over par." So, scoring a 5 on a par 4 hole is 1 over par (+1).
• If a player matches the par, they score a 0 for that hole.

This system helps players and fans quickly assess a golfer's performance during a round.

Understanding Par

Understanding par is fundamental for interpreting scores in golf. "Par" represents the perfect number of strokes a skilled golfer should ideally take to complete a hole or round.

Here's what affects par:

• Length: Longer holes generally have a higher par.
• Difficulty: More challenging holes may also increase par.

Golf courses commonly have pars of 3, 4, or 5 per hole, adding up to a total par for an entire course. For an 18-hole course, this usually sums up to around 70-72 strokes.

Being under or over par can greatly affect a player's rank in a tournament but equally helps in self-evaluation for casual players who want to track their progress.

Evaluating Expressions

Evaluating expressions in mathematics involves interpreting and simplifying an equation to find its value. The key to understanding Jeff's golf score is translating his gameplay into a numerical expression.

Here's the step-by-step breakdown:

• Identify the scoring for each set of holes. For instance, being 1 under par on 6 holes is translated to multiplying 6 by -1, written as 6(-1).
• Do this for all scores: 4(+2), 1(+3), 2(0), and 5(+1).
• The complete expression becomes: \[ 6(-1) + 4(+2) + 1(+3) + 2(0) + 5(+1) \]
• Calculate the result of each multiplication: -6, 8, 3, 0, and 5.
• Add these results together: \[ -6 + 8 + 3 + 0 + 5 \]
• Simplify to get a final answer: 10, meaning Jeff is 10 strokes over par.

Evaluating expressions like this requires careful step-by-step calculations but is very effective in solving real-life problems like understanding golf scores.