can this be solved by multiplying 3/4 times 5? explain.

Question

A cake for a class party was cut into pieces of equal size. There are 5 pieces of cake left. 3/4 of the class still wants cake. What fraction of the cake will be eaten?

Answer 1

I got this stuck in my head, so a math prof friend helped me out. The class size is 4n. But 3/4 of the class has to be able to be fed from 5 pieces, so 3n<5. assuming n is larger than 0 (in which case the cake was cut into 5 pieces), the only number that works is n=1, so 1/4 of the class is one person. That means the cake was cut into 6 (5+1) pieces, 3 more pieces will be eaten to make 4 eaten in all, so 2/6 is left.