System of Equations - Application Problem

Each school district in Texas has a budget by which to operate. School administrators plan spending so that the exprenses for a school are less than the revenue. The greatest yearly exprense for a school is *payroll* for teachers and other staff. The cost of building new schools, buying school buses, or other long-term expenses are called *capital expenses*. Schools may also have to pay out money for loans or to people who have bought bonds, which support the schools. These are called *debt service expenses*.

The amout of revenue, $\displaystyle R$, per student to Texas schools for the 1999-2000 school year to ther 2003-2004 school year can be approximated by

Revenue: $\displaystyle R = 5732(1.025)^t$

where $\displaystyle t$ represents the school year with $\displaystyle t = 0$ corresponding to the 1999-2000 school year. For the same time period, expenses per student for Texas schools can be represented by the following formulas:

Payroll expenses: $\displaystyle P = 115t + 4598$

Capital expenses: $\displaystyle C = 18t + 191$

Debt service expenses: $\displaystyle D = 2t^2 + 8t + 37$

Miscellanueous expenses: $\displaystyle M = 19t + 894$

- Find an equation that represents the total expenses, $\displaystyle E$, per student.

**For this one...would you just add up all the systems of equations above to get the equation that represents the total expenses per student?**

- Graph the models for the revenue per student and the total expenses per student on the same set of coordinate axes.

**I'll graph this...but I just want to make sure I got the right equation representing total expenses per student in the previous question.**

- In which school year is the revenue per student approximately equal to the total expenses per student? Explain.

**Like previous statement before.**

- In which school year is the difference between the revenue per student and the expenses per student the greatest? What is the difference?

**Like previous statement before.**

- In which school year is the percentage that capital expenses are of total expenses the greatest? What is the percentage?

**Like previous statement before.**