Math is Cool

Maggie was part of a math team that competed in a math competition last Friday. One of the boys on her team placed first in the individual. Their team placed 6th over all. Maggie and Kent studied for a couple weeks the stack of story problems she was given for practice. Here, wrap your head around this one: "On a plane, two men together had 135 kilograms of luggage. The first paid $1.35 for his excess luggage and the second paid $2.70 for his excess luggage. Had all the luggage belonged to one person, the excess luggage charge would have been $8.10. At most how many kilograms of luggage is each person permitted to bring on the plane free of additional charge? " --Personally I think it is a trick question and the answer is "Eli Whitney and the cotton gin."