Problem 12 - Beginning and Intermediate Algebra

Question

The average salary in the San Jose, California, area for a chemical engineer is \(\$ 67,841\). The average salary for a database administrator in the same area is \(\$ 75.657 .\) Write an inequality statement using \(<\) or \(>\) comparing the numbers \(67,841\) and \(75,657 .\)

Step-by-Step Solution

Answer

The inequality is \(67,841 < 75,657\).

Step 1: Identify the Salaries

First, identify the two salaries given in the problem. The salary for a chemical engineer is \(\\(67,841\) and the salary for a database administrator is \(\\)75,657\).

Step 2: Compare the Salaries

Compare the two identified salaries. Determine which is greater or lesser. \(67,841 < 75,657\), meaning the chemical engineer's salary is less than the database administrator's salary.

Step 3: Write the Inequality

Now, write the inequality statement based on the comparison. The correct inequality is \(67,841 < 75,657\). This shows that the average salary of a chemical engineer is less than that of a database administrator.

Key Concepts

Average Salaries

In many professions, understanding average salaries is crucial, whether you're planning a career move or negotiating a raise.
The average salary gives an estimate of what someone in a particular job or locality might earn annually.
In the context of the exercise, we are comparing the average salaries of two professions in the San Jose area:

• Chemical Engineer: $67,841
• Database Administrator: $75,657

Average salaries can be influenced by various factors, including location, experience, and company size.
It's important to remember that averages are just that – averages. They give a middle or mean point of a dataset but don't account for higher or lower salary extremes.
Understanding this can help contextualize the numbers when comparing two professions or job roles.

Comparison

When comparing two values, it's essential to understand not just the numbers, but also the context.
The exercise requires us to compare the average salaries of two professions using an inequality statement.
An important aspect of comparison is identifying which value is larger or smaller:

• If one number is larger, we use the symbol '>'.
• If the other number is smaller, we use the symbol '<'.

In the given scenario, we compare $67,841 and $75,657, and find that $67,841 < $75,657.
This tells us that on average, chemical engineers in San Jose earn less than database administrators.
Making these types of comparisons can help with deciding on career paths or understanding salary offers.

Mathematical Symbols

Mathematical symbols simplify complex ideas into digestible information.
In inequalities, symbols like '<' (less than) and '>' (greater than) play a crucial role.

• The symbol '<' indicates that the number on the left is smaller than the number on the right.
• The symbol '>' indicates that the number on the left is greater than the number on the right.

The exercise showcases how to use '<' to compare two salaries effectively.
By writing the inequality statement as \(67,841 < 75,657\), we are able to quickly understand the salary difference without lengthy explanations.
This mathematical shorthand is widely used not only in academics but also in everyday financial and statistical analysis.