Problem 97 - Algebra for College Students

Question

Natasha recorded the daily gains or losses for her company stock for a week. On Monday it gained \(1.25\) dollars; on Tuesday it gained \(0.88\) dollars; on Wednesday it lost \(0.50\) dollars; on Thursday it lost \(1.13\) dollars; on Friday it gained \(0.38\) dollars. What was the net gain (or loss) for the week?

Step-by-Step Solution

Answer

The net gain for the week was $0.88.

Step 1: Understanding Daily Changes

First, identify the daily gains or losses for each day. Monday: +1.25, Tuesday: +0.88, Wednesday: -0.50, Thursday: -1.13, Friday: +0.38.

Step 2: Calculating Total Gains and Losses

Add up all the gains and losses for the week. This means adding the positive and negative values together: \( 1.25 + 0.88 - 0.50 - 1.13 + 0.38 \).

Step 3: Performing the Addition and Subtraction

Calculate the sum step-by-step: First add the gains: \( 1.25 + 0.88 + 0.38 = 2.51 \). Then add the losses as a negative number: \( -0.50 - 1.13 = -1.63 \).

Step 4: Finding the Net Gain or Loss

Subtract the total losses from the total gains: \( 2.51 - 1.63 = 0.88 \). This represents the net gain for the week.

Key Concepts

Stock Market Analysis

Stock market analysis is an essential skill for anyone investing in stocks. It involves examining daily market actions and understanding how different factors affect stock prices. By recording daily changes, investors can keep track of how a stock performs over time.

In stock market analysis, understanding the concepts of gains and losses is crucial. A gain means the stock has increased in value, while a loss indicates a decrease. Investors should pay careful attention to these daily fluctuations as they can add up over time to impact overall investment health. In Natasha's example, daily recording enables the clear visualization of stock trends throughout the week.

This detailed recording is crucial for identifying patterns or major influences on stock prices. By evaluating these daily changes, investors can make better decisions about buying or selling stocks.

Basic Arithmetic Operations

Basic arithmetic operations are foundational skills not just in mathematics, but also in real-world activities, like analyzing stocks. They involve the ability to add, subtract, multiply, and divide numbers.

In Natasha's case, we're focused on addition and subtraction. She had to add gains and subtract losses over a week. This is a practical approach for calculating net gain or loss of her stock.

• Gains: When adding gains, you sum positive numbers, such as \(1.25 + 0.88 + 0.38\).
• Losses: Subtracting losses involves negative numbers. Here, \(-0.50\) and \(-1.13\) were subtracted as \(-1.63\).

Note: Always remember that when you subtract a negative, you are effectively adding a positive value. This is key in understanding how to interpret and calculate stock performances effectively.

Step-by-Step Problem Solving

Step-by-step problem solving is a methodical approach to tackle problems efficiently. It breaks the process down into manageable parts and makes even complicated problems seem easy to solve.

Follow these steps as Natasha did to find her stock's net gain/loss:

• Step 1: Identify what you need to know—in this case, the gains and losses for each day.
• Step 2: Summarize these daily values to get a clear picture of the week's transactions. In Natasha's example, this step involved adding all the daily figures together.
• Step 3: Perform the arithmetic by calculating gains and losses separately, followed by combining these results.
• Step 4: Analyze the outcome to find the net gain or loss, which provides insights into overall performance.

This approach ensures that each step is clear and contributes to the final solution. It is an excellent example of problem-solving in the context of real-world financial scenarios.