Problem 148 - 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 196 strokes and par is 208 .

Step-by-Step Solution

Answer

The golfer's score relative to par is -12.

Step 1: Identify the values

From the exercise, it can be seen that the golfer made 196 strokes (N) and the par is 208 (P).

Step 2: Substitution

Substitute the values into the equation \(S=N-P\). This becomes \(S=196-208\)

Step 3: Perform the calculation

Subtract 208 from 196, which results in -12

Key Concepts

Algebraic Expressions

Understanding algebraic expressions is crucial to solving equations in prealgebra. An algebraic expression is a mathematical phrase that can contain numbers, operators (like addition, subtraction, multiplication, and division), variables (letters that stand for unknown values), and sometimes exponents. For example, in the equation presented in the exercise, S = N - P, 'S', 'N', and 'P' represent variables, and the subtraction operator indicates the operation applied to these variables. Here's how you should interpret it:

• S stands for the golfer's score relative to par.
• N is the number of strokes made by the golfer.
• P represents the par for the course.

In this case, the expression tells us how to calculate the golfer's score by subtracting the par from the number of strokes made. It's essentially a simplified model of the situation represented in a mathematical language.

Substitution Method

The substitution method is a powerful tool in algebra, which involves replacing variables with their actual values to simplify the problem and find the solution. Here's how you can apply this method step by step:

• Identify the variables: Determine what each variable represents. In the exercise, 'N' is 196, and 'P' is 208.
• Substitute the values: Replace the variables in the algebraic expression with the identified values. The expression S = N - P becomes S = 196 - 208.
• Solve: With the variables replaced by actual numbers, you can now accurately solve the equation.

This method turned our abstract algebraic expression into a concrete arithmetic problem that can be easily solved, which in this example would lead to finding out the golfer's score relative to par.

Arithmetic Operations

At the heart of prealgebra are the fundamental arithmetic operations: addition, subtraction, multiplication, and division. These operations are the building blocks for more complex mathematical concepts. Let's go over how to execute these operations correctly:

• For addition: Add up the numbers. If they're positive, the number increases; if one is negative, it decreases.
• For subtraction: Deduct the second number from the first. If you're subtracting a larger number from a smaller one, the result is negative, as seen in the exercise where subtracting 208 (a larger number) from 196 (a smaller number) resulted in -12.
• For multiplication: Multiply the values together. Remember the rule of signs: A positive times a positive or a negative times a negative gives a positive result. In contrast, a positive times a negative gives a negative result.
• For division: Divide the first number by the second, adhering to the same rule of signs as multiplication.

Understanding and applying these operations accurately is essential, especially when working with algebraic expressions and equations in prealgebra.