## Real World Applications – Algebra I

### Topic

What’s the total cost of college?

### Student Exploration

Students will use direct variation to understand the cost of attending a four-year university.

Student will need:

- Access to internet

The Process:

- Research a four-year university you would like to attend.
- On the university’s website, find how much it costs to attend that university each year.
- Create an equation to represent the total cost of attending the university.
- If I only wanted to spend a total of $20,000 on college, how many years would I be able to attend?
- If I wanted spend six years attending this university, how much would it cost?

### Extension Investigation

- During a student’s first two years living on campus at a four-year university, what would the constant of proportionality be? Why?
- Would this be a direct variation relationship? Why or why not?
- What is the equation associated with this relationship?
- What is the difference between the equations of the proportional relationship and not proportional?

#### ANSWERS

Let’s look at a particular university as an example and see the direct variation with the university’s tuition. Duke University is located in North Carolina, and is very competitive with college basketball. For undergraduates at Duke, the total cost to attending one year is $59,343. This is including the undergraduate fees, room and board, and an estimate of books and personal expenses. The information was found here: http://admissions.duke.edu/education/value

If we were to just focus on the tuition and fees, the cost is $40,101. Most students graduate with their bachelor’s degree in four years. We can calculate the total cost of attendance by using a formula with $40,101 as the constant: , where represents the number of years attending the university, and represents the total cumulative cost to go to college. In four years, we would substitute 4 in for in the equation, and solve for . . To attend this university, a person would typically spend $160,404 to graduate on time.