Jada has time on the weekends to earn some money. A local bookstore is looking for someone to help sort books and will pay $12.20 an hour. To get to and from the bookstore on a work day, however, Jada would have to spend $7.15 on bus fare.  

1. Write an equation that represents Jada’s take-home earnings in dollars, , if she works at the bookstore for hours.
2. One day, Jada takes home $90.45 after working hours and after paying the bus fare. Write an equation to represent this situation.
3. Is 4 a solution to the last equation you wrote? What about 7?
   • If so, be prepared to explain how you know one or both of them are solutions.
   • If not, be prepared to explain why they are not solutions. Then, find the solution.
4. In this situation, what does the solution to the equation tell us?

One gallon of gasoline produces about 20 pounds of carbon dioxide. One gallon of pure ethanol produces about 13 pounds of carbon. A car engine that can run on gasoline or ethanol produces 100 pounds of carbon dioxide from gallons of gasoline and gallons of ethanol.
The equation represents the relationship between these quantities.

1. Determine if each pair of values could be the number of gallons of gasoline and ethanol burned in the car engine. Be prepared to explain your reasoning.
   1. 5 gallons of gasoline and 7.7 gallons of ethanol
   2. 3.05 gallons of gasoline and 3 gallons of ethanol
   3. 2 gallons of gasoline and 4.5 gallons of ethanol
2. If the car engine burned 4 gallons of gasoline, how many gallons of ethanol were burned? Show your reasoning.
3. In this situation, what does a solution to the equation tell us? Give an example of a solution.