Problem 97 - Elementary and Intermediate Algebra

Question

Movie Losses. According to the Numbers Box Office Data website, the movie Stealth, released in 2005 by Sony Pictures, cost about \(\$ 176,350,000\) to produce, promote, and distribute. It reportedly earned back just \(\$ 76,700,000\) worldwide. Express the dollar loss suffered by Sony as a signed number.

Step-by-Step Solution

Answer

Sony's dollar loss is \( \$ -99,650,000 \).

Step 1: Understanding Movie Costs and Earnings

To determine the dollar loss, we first need to recognize the two critical numbers involved: the cost to produce, promote, and distribute the movie, which is \( \\( 176,350,000 \), and the earnings from the movie, which is \( \\) 76,700,000 \).

Step 2: Calculating the Loss

The loss can be calculated by subtracting the earnings from the costs. This gives us the formula: \[ \text{Loss} = \text{Cost} - \text{Earnings} \] Substituting the given values gives us: \[ \text{Loss} = \\( 176,350,000 - \\) 76,700,000 \]

Step 3: Performing the Subtraction

By carrying out the subtraction of the earnings from the cost: \[ \\( 176,350,000 - \\) 76,700,000 = \$ 99,650,000 \]

Step 4: Expressing the Loss as a Signed Number

A loss means that the outcome is negative, so the dollar loss will be expressed as a negative value. Therefore, the dollar loss is \( \$ -99,650,000 \).

Key Concepts

Algebra

Algebra is a vital component of mathematics that deals with symbols and the rules for manipulating these symbols. It's essential because it allows us to set up equations that represent real-world situations. In the context of our movie loss problem, we are dealing with the formula:

• \( \text{Loss} = \text{Cost} - \text{Earnings} \)

This equation is a straightforward algebraic expression that helps us calculate the difference between two monetary values. The symbols, in this case "Cost" and "Earnings," represent the amounts involved in the movie's financial outcome.
Algebra allows us to solve for the loss by substituting the actual numerical values into the equation, demonstrating the practical use of algebra in everyday problem-solving. Understanding this usage helps you interpret and solve similar situations where you need to calculate gains, losses, or even break-even points.

Mathematical Subtraction

Mathematical subtraction is a fundamental arithmetic operation that involves taking something away from a total. In our scenario involving the movie 'Stealth,' subtraction helps us find out how much money was lost after expenses were deducted from earnings. The expression for this is:

• \( \text{Loss} = 176,350,000 - 76,700,000 \)

When performing subtraction, it's crucial to align the numbers correctly, ensuring that each digit corresponds to its place value. This process enables accurate calculations.
Subtraction also allows us to determine how one quantity compares to another, especially in financial contexts. It's the method by which we determine shortfalls, such as the difference between planned and actual earnings in financial reporting.

Financial Loss Calculation

Financial loss calculation involves recognizing and expressing the monetary deficit incurred, usually in business or investment scenarios. In the case of 'Stealth,' we calculate how much money Sony lost compared to what they spent. A financial loss is a negative outcome, representing a decrease in value.

• This calculation is performed by subtracting earnings from expenses.
• The result is, therefore, a negative value, indicating loss, which in this case is \( \$ -99,650,000 \).

Expressing the result as a signed number provides clarity that the outcome is less than zero, emphasizing the debt or deficiency.
Understanding financial losses is crucial for businesses to analyze their spending, strategize future investments, and make informed decisions about budgeting.