PS.53 Brother I.D. Ricks is a faculty member at BYU-Idaho whose grandchildren live in Oklahoma and California. He and his wife would like to visit their grandchildren at least once a year in these states. They currently have one vehicle with well over 100,000 miles on it, so they want to buy a newer vehicle with fewer miles and that gets better gas mileage. They are considering two options: (1) a new subcompact car that would cost $18,750 to purchase or (2) a used sedan that would cost $13,150. They anticipate that the new subcompact would get 35 miles per gallon (combined highway and around town driving) while the sedan would get 23 miles per gallon. Based on their road tripping history they expect to drive 18,000 miles per year. For the purposes of their analysis they are assuming that gas will cost $3.23 per gallon.

Question: How many miles would the Ricks need to drive before the cost of these two options would be the same? (Display your answer to the nearest whole number.)

(Hint: The challenge with this problem is finding the variable costs. First determine the variable costs per mile, in terms of gasoline costs. From there you can easily use the break-even formula to find the break-even point in terms of milesand then do some simple math to get the break-even point in years.)

How many years would it take for these two options to cost the same? (Display your answer to two decimal places.)

Suppose a severe disruption to the petroleum supply resulted in a $1.75 increase to the price of gasoline. How many miles would it now take before the cost of these two options would be the same? (Display your answer to the nearest whole number.)