On a hike to the outdoor math arena, twelve high school mathletes carried ten loaves of bread. Each B-team mathlete carried one loaf, each A-team mathlete carried a half loaf; and each varsity mathlete carried a quarter loaf. How many mathletes from each team were there, assuming that there was at least one from each team?
Solution
Well, it takes 1 A-team and 2 varsity mathletes to carry a total of 1 loaf. To carry 10 loaves, the remaining 9 mathletes must all be on the B-team.
When they arrive at the arena, the B-team confronts the other two teams about the unfair division of labor. The mathletes agree to dissolve their hierarchal practices. The bread is shared among all so that each receives what they need.
PS: Might there be another solution?
PPS: If you stop to think about it, this problem is ridiculous, even though there is a disclaimer about unfair labor practices. You might want to give students extra credit if they can re-cast the problem as another situation that makes more sense. If any of your students go for it, and if they come up with something that you like, please get in touch with us. We'd be glad to give credit where credit is due.