Question

Mr. Dietz is a teacher whose salary is \(\$ 22,570\) for this school year, which has 185 days. In Mr. Dietz's school district, substitute teachers are paid \(\$ 80\) per day. If Mr. Dietz takes a day off without pay and a substitute teacher is paid to teach Mr. Dietz's classes, how much less does the school district pay in salary by paying a substitute teacher instead of paying Mr. Dietz for that day? A. \(\$ 42\) B. \(\$ 80\) C. \(\$ 97\) D. \(\$ 105\) E. \(\$ 122\)

Short answer

Answer: $42

Step-by-step solution

Find Mr. Dietz's daily salary

To find Mr. Dietz's daily salary, we need to divide his annual salary by the number of school days in the year. His annual salary is \(\$22,570\) and there are 185 school days in the year. So we have to calculate: Mr. Dietz's daily salary = \(\frac{\$22,570}{185}\)

Calculate Mr. Dietz's daily salary

Divide the given amount \(22,570\) by 185 school days: Daily salary = \(\frac{22570}{185} = \$122\)

Compare Mr. Dietz's daily salary with the substitute teacher's daily salary

Now we have Mr. Dietz's daily salary of \(122. The substitute teacher's daily salary is \)80. We need to find the difference in the cost for the school district: Difference = \(122 - 80\)

Calculate the difference in cost for the school district

Now subtract the two salaries to find the difference in cost for the school district when a substitute is paid instead of Mr. Dietz: Difference = \(122 - 80 = \$42\)

Choose the correct answer

The difference in cost for the school district when a substitute teacher is paid instead of Mr. Dietz for that day is \(\$42\). This matches with option A, so the correct answer is: A. \(\$42\)

Key concepts

Substitute Teacher Pay

Understanding how substitute teacher pay is determined can be essential for grasping the financial decision-making process in education. Substitute teachers typically earn a set amount per day, regardless of the regular teacher's salary. This rate is often significantly lower than the daily rate of a full-time teacher with an annual salary.

For example, in the exercise involving Mr. Dietz, we calculate that a substitute teacher is paid \(80 per day, while Mr. Dietz's daily earnings, once broken down from his annual salary, come out to \)122. This significant cost difference can impact a school district's budget, especially over many instances of teachers being absent. Substitute teacher pay policies can vary widely by district but are an important part of educational finance sensibility and resource allocation.

Educational Finance

Educational finance is a cornerstone of how school districts operate, determining everything from building maintenance to teacher salaries. Educators like Mr. Dietz are compensated based on annual contracts that define salaries over a set number of working days, in this case, 185. To understand the full picture of educational finance, it's critical to consider both the fixed costs, such as teacher salaries, and variable costs, like substitute pay.

Another important factor in educational finance is how salaries are funded. In most cases, public school funding comes from a combination of local property taxes, state funds, and federal assistance, each carrying differing stipulations on how the money can be used.

School District Budgeting

School district budgeting ties directly into the concepts of teacher pay and educational finance. Establishing a budget requires careful planning and forecasting to allocate funds for fixed costs, like Mr. Dietz's salary, while also setting aside resources for unpredictable expenses such as substitute teacher pay.

Each district must manage its budget to ensure that there are enough substitute teachers available when regular teachers are absent, without overspending. Cost-saving measures, like the one illustrated in Mr. Dietz's scenario, help maintain financial stability within a school district. This intricate balancing act ensures that quality education is delivered consistently, while financial resources are utilized efficiently.