If You are considering the purchase of a new car Your choice

If You are considering the purchase of a new car. Your choice is a fuel-efficient Toyota Prius for $21,100 or lower-cost Hyundai Accent for $12,925. The Prius gets 47 mpg (miles per gallon of gasoline) and the Accent gets 33 mpg. How many miles would you have to drive to make the two purchases equivalent? Assuming a gasoline price of $1.90/gallon.

Solution

Let x = miles driven
.
Prius cost:
21100 + 1.90(x/47)
.
Accent cost:
12925 + 1.90(x/33)
.
Set the costs equal to each other and solve for x:
21100 + 1.90(x/47) = 12925 + 1.90(x/33)
21100 + 1.90(x/47) = 12925 + 1.90(x/33)
8175 + 1.90(x/47) = 1.90(x/33)
Multiplying both sides by a common denominator say (47)(33) we get:
12679425 + 62.7x = 89.3x
12679425 = 26.6x
476,670.113 miles = x