Problem 147 - Prealgebra and Introductory Algebra

Question

Golf Use the equation \(S=N-P,\) where \(S\) is a golfer's score relative to par in a tournament, \(N\) is the number of strokes made by the golfer, and \(P\) is par, to find a golfer's score relative to par when the golfer made 49 strokes and par is 52 .

Step-by-Step Solution

Answer

The golfer's score relative to par is -3

Step 1: Understand the Equation

In the given equation \(S=N-P\), \(S\) denotes a golfer's score relative to par, \(N\) is the number of strokes the golfer made, and \(P\) is the par.

Step 2: Insert the Given Values

Now, substitute \(N=49\) and \(P=52\) into the given equation. The new equation becomes \(S=49-52\)

Step 3: Simplify the Equation

Finally, subtract 52 from 49, which will give you the value of \(S\), \(S=49-52=-3\)

Key Concepts

Solving Equations

Solving equations is a fundamental concept, especially in prealgebra, where we deal with finding unknown values from known values. The goal is to isolate the variable of interest on one side of the equation.
In the context of our golf score exercise, we are dealing with a simple algebraic equation:

• The equation provided is \(S = N - P\). Here, \(S\) represents the unknown variable, which is the golfer's score relative to par. \(N\) and \(P\) are known values.
• By substituting the known values into the equation — \(N = 49\) and \(P = 52\) — the problem becomes straightforward, with the equation changing to \(S = 49 - 52\).
• The next step is to perform the arithmetic calculation to solve for \(S\), the score relative to par.

Solving equations like this one is about replacing variables with numbers and performing the basic arithmetic tasks. The result gives us the value of the unknown variable.

Subtraction

Subtraction is one of the basic operations in mathematics and is used to find the difference between two numbers. In the previous section, we learned that substitution helped us transform the equation for the golf score into a simple subtraction problem.
Subtraction involves taking away one number from another:

• In our example, we subtract the number of par strokes \(P\) (52) from the actual strokes \(N\) (49) the golfer made during the tournament.
• The equation \(S = 49 - 52\) illustrates this, where we compute the difference between 49 and 52.
• The result of the subtraction \(49 - 52\) is \(-3\), which tells us the golfer's score relative to par.

Remember, the result can be a negative number, as here, indicating that the golfer scored under par, which is typically good in golf.

Golf Score Calculation

Understanding how to calculate a golf score using the provided formula is important for clarifying the relative performance of golfers.
Golfers aim to complete each hole in fewer strokes than the set par number. This performance is measured by their score relative to par:

• The equation \(S = N - P\) allows us to see how many strokes a golfer took compared to what is considered average or par.
• In this golf score calculation, \(N = 49\) is the total actual strokes taken by the golfer, and \(P = 52\) is the par for the tournament.
• Since the result \(S = -3\), it indicates the golfer completed the course 3 strokes below par.

This kind of calculation reflects skill and efficiency in the game. Lower scores relative to par suggest a more proficient performance by the golfer.