Question

Marsha bakes a cake for a party. Several guests take 1/3rd of the cake and split it. A few more guests take half of what is left and split that. Marsha takes a third of the remaining cake for herself. If Marsha evenly divides what is left of the cake between the 4 remaining guests, what fraction of the original cake will each of them receive?

Answer 1

1/18.

Explanation:

Firstly 1 - 1/3 = 2/3 left

Now 1/2 of 2/3 is taken to leave 2/3 - 2/3 * 1/2 = 1/3.

Marsha takes 1/3 of 1/3 = 1/9 so now there is 1/3 = 1/9 = 2/9 left.

So the 4 remaining guests will receive 2/9 * 1/4 = 2/36

= 1/18 of the cake.