Question 1037623: You are planning to purchase a new car and have narrowed down your search to two models:
2016 Toyota Prius costs 26800 and gets an average of 50 miles per gallon
2016 Toyota Corolla costs 17900 and gets an average of 32 miles per gallon
In either case, the dealer has offered 0% financing, and you can afford the monthly payments for either car. Assume that all costs of ownership are the same (taxes, insurance, maintenance, etc.) If gas costs 2.40 per gallon, how many miles would you have to drive for the total cost (purchase price and fuel used) of the two cars to be equal?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! prius costs 26800 and gets 50 mpg.
corolla costs 17900 and gets 32mpg.
gas costs 2.40 per mile.
let x = number of miles driven.
total cost for prius would be 26800 + 2.40 * x / 50.
total cost for corolla would be 17900 + 2.40 * x / 32.
the cost is the same when both these equations are equal to each other.
you get 26800 + 2.40 * x / 50 = 17900 + 2.40 * x / 32.
simplify to get 26800 + .048 * x = 17900 + .075 * x
subtract .048 * x from both sides of the equation and subtract 17900 from both sides of the equaiton to get 26800 - 17900 = .075 * x - .048 * x.
combine like terms to get 8900 = .027 * x
divide both sides of the equation by .027 and solve for x to get x = 8900 / .027 = 329629.6296 miles.
both cars would have to travel 329629.6296 miles each in order for you to break even.
the prius would cost 26800 + 2.40 * 329629.6296 / 50 = 42622.22222.
the corolla would cost 17900 + 2.40 * 329629.6296 / 32 42622.22222.
anything less than that and the prius costs more.
anything more than that and the corolla costs more.
for example, assume 100,000 miles.
prius would cost 26800 + 2.40 * 100000/50 = 31600.
corolla would cost 17900 + 2.40 * 100000/32 = 25400.
if you just look at the difference in cost between the prius and the corolla, that difference is 26800 - 17900 = 8900 dollars.
the savings in gas cost per mile would have to be equal to that in order to make the costs the same.
the difference in the cost of gas per mile is 2.40 / 50 for the prius versus 2.40 / 32 for the corolla.
that becomes .048 versus .075 or a savings of .027 per mile for the prius over the corolla.
divide 8900 by .027 and you get 329629.6296 miles.
the algebraic equation tells you the same thing.
you can also solve this graphically.
equation for the prius is 26800 + 2.40 / 50 * x.
equation for the corolla is 17900 + 2.40 / 32 * x.
the intersection of the graph of the two equations tells you the break even point.
the graph is shown below.
the blue line is the corolla and the red line is the prius.
before x = 329629 the corolla is cheaper because the blue line is beneath the red line.
after x = 329629 the prius is cheaper because the red line is beneath the blue line.
the break even point is at x = 329629, as shown on the graph.
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