Problem 101 - Intermediate Algebra

Question

Write a numerical statement to represent the problem. Then simplify the numerical expression to answer the 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 \(0.88\) dollar; on Wednesday it lost \(0.50\) dollar; on Thursday it lost \(1.13\) dollars; on Friday it gained \(0.38\) dollar. 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 the Stock Gains and Losses

Read the problem carefully to understand that we need to calculate the net gain or loss for Natasha's company stock over the week. Daily changes are recorded as gains or losses on each day of the week.

Step 2: Set Up the Numerical Expression

Write a numerical expression incorporating each day's gain or loss: \[ 1.25 + 0.88 - 0.50 - 1.13 + 0.38 \].Each number represents the gain or loss for that day: Monday, Tuesday, Wednesday, Thursday, and Friday, respectively.

Step 3: Simplify the Expression

Start by grouping and combining the numbers. First, add the gains:\[ 1.25 + 0.88 + 0.38 = 2.51 \].Next, add the losses:\[ 0.50 + 1.13 = 1.63 \].

Step 4: Calculate the Net Gain or Loss

Subtract the total losses from the total gains to find the net result:\[ 2.51 - 1.63 = 0.88 \].This result represents the net gain or loss for the week.

Key Concepts

Stock Gains and Losses

Stock gains and losses are crucial concepts in the world of investing and day-to-day trading. When you own stocks, their value can fluctuate due to market conditions, company performance, and other factors. These fluctuations are often recorded as gains or losses.

• A gain represents an increase in the stock's value. For example, if a stock's price rises from $10 to $15, the gain is $5.
• A loss occurs when the stock's price drops. For instance, if a stock's price falls from $20 to $18, the loss is $2.

Understanding gains and losses helps investors make informed decisions about buying or selling their stocks. In the exercise, Natasha's company experiences daily variations in stock prices, which must be tracked to find out the total financial impact over a period, such as a week.

Net Gain or Loss

Net gain or loss is the final amount you get after accounting for all gains and losses over a specified period. It's a critical indicator of whether an investment has increased or decreased in value.
Calculating the net gain or loss involves adding all the gains and subtracting all the losses during that period. This calculation is straightforward yet powerful, as it provides a comprehensive picture of financial performance. In Natasha's case, the task is to calculate the total impact on stock value over a week.
When there are:

• More gains than losses: The net result is a net gain, indicating a positive investment increase.
• More losses than gains: The net result is a net loss, revealing a decrease in investment value.

In the provided example, the week's stocks had a net gain, meaning Natasha's company value increased slightly over those five days.

Simplifying Expressions

Simplifying expressions involves reducing a numerical statement to its simplest form. This often includes combining like terms and performing arithmetic operations to reach a concise answer. This process is essential in solving many mathematical problems, and it's especially useful in financial calculations to quickly assess the outcome.
In the context of Natasha's stock problem, you simplify expressions by:

• Grouping like terms: Combine all gains into one sum and all losses into another.
• Performing arithmetic: Subtract the total losses from the total gains to find the net result.

The simplification process helps interpret the cumulative financial effect over the week, making it easier to present the data in a clear and understandable way. Ultimately, the simplified expression in the exercise provided a clear picture by confirming a net gain of $0.88, thus accurately reflecting Natasha's stock outcomes for the week.