Mr. Algebra baked a cake for the Midwest Mathematics Convention. He designed the cake in the shape of a big cube. As he was carrying the cake over to the frosting table, he slipped and sent the cake sailing into the vat of frosting.
Amazingly, the cake stayed in one piece, but all 6 sides were now frosted. He carefully got it out and put it on a platter.
The mathematicians were delighted when they saw the cube–cake with all sides frosted. One mathematician suggested the cake be cut into cube shaped pieces, all the same size. That way, some people could have a piece with no frosting, 1 side frosted, 2 sides frosted, or 3 sides frosted. Kawana, a very creative mathematician, said, "Cut the cake so that the number of pieces with no frosting is eight times more than the number of pieces with frosting on 3 sides. Then you will have the exact number of pieces of cake as there are mathematicians in this room."
Your Task:
(1) Using Kawana's clue, find out how many mathematicians were at the convention. Hint: build models of different size cakes.
(2) How many mathematicians would be at the convention if the number of pieces with 1 frosted side equaled the number of pieces with no frosting?
2007-03-04
06:38:20
·
2 answers
·
asked by
dorkified at heart
1
in
Mathematics