Lesson 15, Part C, Solving equations Theme: Risk Assessment Solving equations such as blood alcohol content (BAC) and proportional equations for resizing graphics is an important skill. Mathematical models are often constructed to represent real-life situations. Being able to use these equations fully includes being able to solve for unknown variables in the equation. Below are two scenarios for you to practice and enhance your equation-solving skills. With each problem, check that the answer is reasonable, given the context, and that you have included the correct units with your solution. Credit: Maridav/Shutterstock Objectives for the lesson You will understand that: O Many equations can be solved by following the basic rules of undoing and keeping the equation balanced. You will be able to: O Solve equations that require simplification before solving. O Solve for a variable in terms of other variables. Paula has two options for going to school. She can carpool with a friend or take the bus. 1) Her friend estimates that driving will cost 22 cents per mile for gas and 8.2 cents per mile for maintenance of the car. Additionally, there is a $25 parking fee per week at the college. If Paula carpools, she would pay half of these costs. The cost of the carpool can be modeled by the following equation, where C is the cost of carpooling per week and m is the total miles driven to school each week: C = (0.082m + 0.22m + 25) %3D Part A: Explain what each term in the equation represents. Part B: Find the total weekly carpooling cost if the commute to school is 7 miles each way and Paula goes to school three times a week. Part C: A weekly bus pass costs $22.00 dollars. How many total miles must Paula commute to school each week for the carpool cost to be equal to the bus pass? How many trips to school each week must Paula make for the bus pass to be less expensive than carpooling? Copyright © 2016, The Charles A. Dana Center at the University of Texas at Austin