Problem 100 - Elementary and Intermediate Algebra

Question

U.S. Jobs. The table lists the three occupations that are predicted to have the largest job declines from 2008 to 2018 . Complete the column labeled "Change." $$ \begin{array}{|c|c|c|} \hline & {\text { Number of jobs }} \\ \hline \text { Occupation } & {2008} & {2018} & {\text { Change }} \\ \hline \text { Farmers/ranchers } & {985,900} & {906,700} \\ \hline \text { Sewing machine operators } & {212,400} & {140,900} \\ \hline \text { Order clerks } & {245,700} & {181,500} \\ \hline \end{array} $$

Step-by-Step Solution

Answer

Farmers/Ranchers: 79,200; Sewing Machine Operators: 71,500; Order Clerks: 64,200.

Step 1: Understand the Task

We need to calculate the change in the number of jobs for each occupation from 2008 to 2018. The change is calculated by subtracting the number of jobs in 2018 from the number of jobs in 2008.

Step 2: Calculate Change for Farmers/Ranchers

Subtract the number of jobs in 2018 (906,700) from the number of jobs in 2008 (985,900).\[\text{Change for Farmers/Ranchers} = 985,900 - 906,700\]

Step 3: Calculate Change for Sewing Machine Operators

Subtract the number of jobs in 2018 (140,900) from the number of jobs in 2008 (212,400).\[\text{Change for Sewing Machine Operators} = 212,400 - 140,900\]

Step 4: Calculate Change for Order Clerks

Subtract the number of jobs in 2018 (181,500) from the number of jobs in 2008 (245,700).\[\text{Change for Order Clerks} = 245,700 - 181,500\]

Step 5: Finalize Results

Record the calculated changes: \[\text{Farmers/Ranchers: 79,200}\] \[\text{Sewing Machine Operators: 71,500}\] \[\text{Order Clerks: 64,200}\]

Key Concepts

Job Decline Calculations

When analyzing job trends over a period, it's important to understand how to calculate job decline effectively. Job decline calculations involve determining the decrease in the number of jobs in a particular occupation between two different years. This process is straightforward, involving basic subtraction. You find the difference by subtracting the future job count from the past job count for the same occupation.

For example, in the given exercise, you calculate the decline in jobs for various occupations over a 10-year period. Each calculation follows this formula:

• Identify the job numbers in two different years.
• Subtract the later job count (2018) from the earlier job count (2008).
• The result is the net job decline for the occupation.

Let's put it into perspective with real numbers: For farmers/ranchers, subtract 906,700 (2018 figure) from 985,900 (2008 figure) to get a decline of 79,200 jobs.

These calculations are crucial in workforce planning and policy making, providing insight into occupational trends and economic shifts.

Basic Arithmetic

Basic arithmetic is foundational to solving many everyday problems, including understanding workforce changes over time. The arithmetic operations you would typically use for job decline calculations are subtraction and occasionally addition if comparisons or path measurements over several time points are required.

Subtraction is particularly useful here. You use it to find differences, like how we determine the decline in each occupation from 2008 to 2018. Here's a clear walkthrough using subtraction:

• For sewing machine operators, start with the number of jobs in 2008: 212,400.
• Subtract the 2018 count: 140,900.
• Your subtraction yields 71,500, representing the job loss for that period.

Understanding subtraction as "taking away" facilitates grasping this concept intuitively. Always double-check calculations to ensure accuracy—a key practice in real-world applications.

Applied Mathematics

Applied mathematics involves the use of mathematical methods and formulas to solve practical problems in various domains, including economics, engineering, and, relevant here, labor market analyses. This approach helps translate numerical data into meaningful insights about employment trends and physical changes over time.

In applied mathematics, you convert abstract mathematical principles into tangible solutions, such as visualizing trends or projecting future needs. Having calculated job declines in our example, applied mathematics gives us the tools to:

• Interpret these figures in terms of socioeconomic impact.
• Use patterns to inform policy or individual career decisions.
• Advise on educational programs or training initiatives based on future occupational demands.

By employing simple calculations like subtraction, you utilize applied mathematics to address complex problems with effective, data-driven solutions. This integration of mathematics and real-world situations highlights its value in everyday decision-making and policy formulation.