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# Introduction to Models and Applications

### Learning Outcomes

By the end of this section, you will be able to:
• Write a linear equation to express the relationship between unknown quantities.
• Write a linear equation that models two different cell phone packages.
• Use a linear model to answer questions.
• Set up a linear equation involving distance, rate, and time.
• Find the dimensions of a rectangle given the area.
• Find the dimensions of a box given information about its side lengths.
College students taking an exam. Credit: Kevin Dooley
Josh is hoping to get an A in his college algebra class. He has scores of 75, 82, 95, 91, and 94 on his first five tests. Only the final exam remains, and the maximum of points that can be earned is 100. Is it possible for Josh to end the course with an A? A linear equation will give Josh his answer. Many real-world applications can be modeled by linear equations. For example, a cell phone package may include a monthly service fee plus a charge per minute of talk-time; it costs a widget manufacturer a certain amount to produce x widgets per month plus monthly operating charges; a car rental company charges a daily fee plus an amount per mile driven. These are examples of applications we come across every day that are modeled by linear equations. In this section, we will set up and use linear equations to solve such problems.