Problem 40 - Prealgebra

Question

Jaime's golf score was \(-9\) today. She decreased her score by 5 strokes from yesterday. Which of the following techniques might you use to determine what her golf score was yesterday? Justify your selection(s). Then use the technique(s) to solve the problem.

Step-by-Step Solution

Answer

Jaime's score yesterday was -4.

Step 1: Understand the Problem

We know Jaime's golf score today is -9, and she decreased her score by 5 strokes from yesterday. Our task is to determine her score yesterday by adding the strokes she reduced to today's score.

Step 2: Set Up the Equation

Let's denote Jaime's score yesterday as \( x \). Since her score decreased by 5 strokes to reach \(-9\) today, we can express this as: \( x - 5 = -9 \).

Step 3: Solve for Yesterday's Score

To find \( x \), rearrange the equation to isolate \( x \) on one side: \( x = -9 + 5 \).

Step 4: Calculate the Result

Add the two numbers: \(-9 + 5 = -4\). Therefore, Jaime's score yesterday was \(-4\).

Step 5: Verify the Solution

To verify, subtract 5 from yesterday's score \(-4\), checking it equals today's score: \(-4 - 5 = -9\), which matches Jaime's score today.

Key Concepts

Solving Equations

The process of solving equations is like unraveling a puzzle. Each algebraic equation presents a relationship between numbers and variables, in which we typically seek the value of the unknown variable that makes the equation true. The goal is to isolate the variable so we can clearly see its value. Let's break this down step by step using a simple equation related to the problem of finding Jaime's golf score from yesterday.Imagine an equation like Jaime's, which states her score decreased by 5 strokes to reach \( -9 \): \( x - 5 = -9 \). Here, \( x \) represents her score yesterday.To solve this:

• Add \( 5 \) to both sides of the equation to cancel out the \( -5 \) and simplify the equation to find \( x \).

This results in \( x = -9 + 5 \). By simplifying this, you determine \( x = -4 \). The mastery of solving equations lies in performing operations equally on both sides to maintain the balance of the equation. This helps discover the unknown variable's value.

Negative Numbers

Negative numbers can initially be tricky, especially when they are part of everyday scenarios, like scoring in sports or finances. In Jaime's golf score problem, we encounter negative numbers naturally, with her current score being \( -9 \).When working with negative numbers, it’s crucial to remember:

• Adding a negative number is equivalent to subtraction.
• Subtracting a negative is like adding, as the two negatives cancel each other out.

In our problem, the equation \( x - 5 = -9 \) involves adding \( 5 \) to \( -9 \), which can feel counterintuitive at first. Performing the operation:

• Add \( 5 \) to \( -9 \)

This results in \( -9 + 5 = -4 \). Visualize this on a number line to aid understanding: starting at \( -9 \) and moving 5 steps to the right, landing at \( -4 \).Familiarity with negative numbers makes calculations precise, as they often appear in various mathematical concepts.

Basic Algebra

Basic algebra sets the foundation for many math problems, providing tools to manipulate expressions and solve equations efficiently. In Jaime's exercise, we face a straightforward algebraic equation demonstrating the importance of basic algebraic skills.The key steps include:

• Identifying the variable, such as \( x \) in Jaime's score from yesterday.
• Setting up the equation based on the problem statement: \( x - 5 = -9 \).
• Applying algebraic operations to solve for \( x \).

Through rearranging the equation by adding \( 5 \) to both sides, it forms \( x = -4 \). Here, adding and subtracting allows us to isolate the variable. This highlights two essential elements: recognizing how to set up an equation based on a word problem and knowing how to manipulate it properly. Mastering such basics equips students with problem-solving strategies applicable beyond math, into areas like physics or computer science. It's essential to practice regularly for proficiency. Basic algebra is thus a building block for advanced topics.