Problem 59 - Algebra 1

Question

A major athletic footwear company had about \(\$ 3750\) million in sales of athletic footwear during the year ending May 31,1997 . The company's sales fell to about \(\$ 3500\) million in \(1998 .\) By how much did the company's sales decrease?

Step-by-Step Solution

Answer

The company's sales decreased by \$250 million from 1997 to 1998.

Step 1: Understand the problem

The problem is asking how much the sales of a company decreased from one year to another. In 1997, the company's sales were \$ 3750 million, and in 1998 they fell to \$ 3500 million. The difference between the sales in these two years represents how much the sales decreased.

Step 2: Subtract the sales in 1998 from the sales in 1997

To find the decrease in sales, subtract the amount of sales in 1998 from the sales in 1997: \(\$ 3750\) million - \(\$ 3500\) million.

Step 3: Perform the subtraction

Performing the subtraction gives \(\$ 3750\) million - \(\$ 3500\) million = \(\$ 250\) million.

Key Concepts

Understanding Problems

When you first encounter a math problem, like the one about the sales at a footwear company, it's important to break down what is being asked. In this exercise, we're trying to figure out how much the company's sales decreased from one year to the next. This means we're searching for a change or difference in sales figures. To fully grasp the problem, it's helpful to focus on these initial details:

• Identify what the numbers given represent. In this case, they are sales figures from two different years.
• Determine what you are tasked with finding. Here, it's the decrease in sales from 1997 to 1998.

Once you understand these elements, the problem becomes clearer, and you're prepared to move on to solving it.

Sales Decrease Calculation

After understanding what the problem is about, the next step is to calculate the decrease in sales. You do this by finding the difference between the sales figures of two years. This involves looking at the initial sales figure and subtracting the final sales figure from it.For our example with the athletic footwear company:

• The sales in 1997 were \(\\( 3750\) million.
• By 1998, the sales decreased to \(\\) 3500\) million.

To find how much the sales decreased, you simply subtract the sales of 1998 from the sales of 1997. This process of calculating the change is not only crucial for such exercises but is also widely used in real-world business scenarios to report financial performance.

Year-to-Year Comparison

A year-to-year comparison involves looking at two sets of data, typically from consecutive years, to analyze changes over time. This is often used in financial contexts to assess how a company is performing. In our exercise, we're comparing sales figures from 1997 and 1998. This kind of comparison is essential because:

• It helps in understanding trends, whether things are improving or declining.
• It provides a basis for forecasting future trends and identifying areas of growth or concern.

By comparing the sales of 1997 and 1998, you can clearly see the decrease. This understanding can inform decisions about strategic changes or improvements needed to boost sales in the future.

Integer Subtraction

The process of subtraction in this problem is simple and relies on basic integer subtraction. This concept involves taking a smaller number away from a larger one to find out the difference between them.Let's apply this to our problem:

• The larger number is the sales for 1997, \(\\( 3750\) million.
• The smaller number is the sales for 1998, \(\\) 3500\) million.
• Subtract the smaller number from the larger one: \(\\( 3750 - \\) 3500 = \\( 250\) million.

The result, \(\\) 250\) million, shows the amount by which the sales decreased. Integer subtraction is a fundamental mathematical operation and is handy in numerous situations, making it a valuable skill for problem-solving.