Problem 117 - Beginning and Intermediate Algebra

Question

The table gives scores (above or below par-that is, above or below the score "standard") for selected golfers during the 2017 Blue Bay LPGA Tournament. Write a signed number that represents the total score (above or below par) for the four rounds for each golfer.

Step-by-Step Solution

Answer

Sum the four scores for each golfer to find the total as a signed number.

Step 1 - Understand the Table

Review the table to see the scores of selected golfers for each of the four rounds. Each score represents how many points above or below par (standard) the golfer scored for that specific round.

Step 2 - Identify Scores for Each Golfer

Identify the individual scores for each of the four rounds for each golfer from the table.

Step 3 - Sum the Scores for Each Golfer

Add the scores from the four rounds for each golfer. Make sure to keep track of positive and negative values correctly during the addition.

Step 4 - Write the Result as a Signed Number

The total score should be written as a signed number, indicating whether it is above (+) or below (-) par.

Key Concepts

addition of integers

When we talk about the addition of integers, we consider both positive and negative numbers. These types of numbers can combine in different ways. For instance, adding two positive numbers will always give a positive result. Conversely, adding two negative numbers will yield a negative result. When you add a positive and a negative number, the outcome depends on their absolute values (the number without its sign). Here are some simple examples:

• Positive + Positive: 5 + 3 = 8
• Negative + Negative: -4 + (-6) = -10
• Positive + Negative: 7 + (-2) = 5
• Negative + Positive: -3 + 9 = 6

In algebra, understanding these rules helps ensure we accurately combine scores or values, especially in word problems like the golf scores example.

signed numbers

Signed numbers include both positive and negative numbers. Positive numbers are those greater than zero (like 1, 5, 100), and negative numbers are less than zero (like -1, -5, -100). The sign of a number tells us its direction on the number line. Positive numbers are to the right of zero, and negative numbers are to the left.

Working with signed numbers involves keeping track of their signs during operations. For instance, when adding -3 and 4:

• Start at -3 on the number line.
• Move 4 units to the right.
• You end up at 1.

This concept is crucial when summing scores in activities like sports, where a golfer’s scores can be above or below a set standard.

summation

Summation means the process of adding a sequence of numbers. In mathematics, summation allows us to combine multiple values into a single number, usually represented by the symbol \(\Sigma\) (capital sigma).

For the exercise given, summation involves adding the golfer's scores from all four rounds. Here’s a step-by-step outline when we sum these scores:

• Identify the individual scores for each round.
• Apply the addition of integers rules.
• Sum all the scores to get a final number.
• Write the result as a signed number, noting if it is above or below par.

By carefully summing each round's scores, we determine the golfer's overall performance relative to par.