Problem 76 - Beginning and Intermediate Algebra

Question

Tyson Industries stock posted a loss of 1.625 points yesterday. If it drops another 0.75 point today, find its overall change for the two days.

Step-by-Step Solution

Answer

The overall change is a loss of 2.375 points.

Step 1: Understand the problem

We need to determine the total change in Tyson Industries stock over two days. The stock lost 1.625 points yesterday and drops by another 0.75 points today.

Step 2: Represent the changes as a sum

The overall change can be calculated by adding the change from yesterday to the change from today. Represent this as an equation: \(-1.625 + (-0.75)\).

Step 3: Calculate the sum

Add the two negative values: \(-1.625 + (-0.75) = -2.375\). This represents the total change in the stock value over the two days.

Step 4: Interpret the result

The negative sign in the result, \(-2.375\), indicates a loss. Hence, the overall change in stock points for Tyson Industries is a loss of 2.375 points.

Key Concepts

Addition of Negative Numbers

Adding negative numbers might seem tricky at first, but it's actually quite simple once you understand the concept. When you have a negative number and you add another negative number to it, you're essentially doing addition in reverse. Here’s how it works:

• When you add two negative numbers, you shift further in the negative direction on a number line.
• The result is a negative number that represents a decrease or loss.

For example, if you start at \(-1.625\) and add \(-0.75\), you move 0.75 units further into the negatives, ending at \(-2.375\). This means, instead of gaining value, we lose even more.

Integer Operations

Integer operations include addition, subtraction, multiplication, and division of whole numbers and their negative counterparts. Understanding these operations is crucial for solving problems involving integers. When dealing with integers:

• Addition of a positive and a negative integer involves determining which number is larger in absolute terms and using its sign as the direction.
• Addition of two negative integers results in a more negative number. You combine their absolute values for the sum, then prefix with a negative sign.

For example, when combining \(-1.625\) and \(-0.75\), the absolute values \(1.625\) and \(0.75\) are added to give \(2.375\), and since both numbers are negative, the result is \(-2.375\).

Problem-Solving Steps

Problem-solving in algebra often involves breaking down problems into manageable steps. This method helps in understanding what is required without getting overwhelmed. Let's take a look at a step-by-step approach:1. **Understand the Problem:** Identify what is being asked. In our scenario, it's about finding the overall change in stock value over two days.2. **Translate into Mathematical Terms:** Convert the problem into an algebraic expression. For this problem, the losses on each day are added together, represented by \(-1.625 + (-0.75)\).3. **Carry Out the Calculation:** Perform the necessary mathematical operations. Here, adding the two negative numbers gives \(-2.375\).4. **Interpret the Result:** Determine what the result tells you. A solution of \(-2.375\) indicates a total loss over the two days. Interpreting results correctly is crucial for drawing meaningful conclusions.