Ellen must decide between two cameras. The first camera costs $47.00 and uses two alkaline AA batteries. The second camera costs $59.00 and uses one $4.95 lithium battery. She plans to use the camera frequently enough that she probably would replace the AA batteries six times a year for a total cost of $11.50 per year. The lithium battery, however, will last an entire year.
a. Let x represent the number of years, and let y represent the cost in dollars. Write an equation to represent the overall expense for each camera.
b. Which camera is less expensive in the short term? In the long term? How long will it take until the overall cost of the less expensive camera is equal to the overall cost of the other camera?