Problem:
In some countries, automobile fuel efficiency is measured in liters per 100 kilometers while other countries use miles per gallon. Suppose that 1 kilometer equals m miles, and 1 gallon equals l liters. Which of the following gives the fuel efficiency in liters per 100 kilometers for a car that gets x miles per gallon?
Answer Choices:
A. 100lmx​
B. 100xlm​
C. 100xlm​
D. xlm100​
E. x100lm​
Solution:
Because the car can travel x miles per gallon, it uses x1​ gallons per mile. This can be converted to liters per 100 kilometers by multiplying by fractions equivalent to 1 , treating units as factors and canceling common factors:
x1​ miles gallons ​=x1​⋅ miles gallons ​⋅1 kilometers m miles ​⋅1 gallons ℓ liters ​⋅100100​=(E)x100ℓm​​100 kilometers liters ​
The problems on this page are the property of the MAA's American Mathematics Competitions