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)x100ℓm100 kilometers liters
The problems on this page are the property of the MAA's American Mathematics Competitions