My sister, Sarah, and I used to have a great time playing with Skittles. First w

Question

My sister, Sarah, and I used to have a great time playing with Skittles. First we would place them in groups on a blanket on the living room floor. Then we would pretend that they were rabbits and we were hawks. We would swoop down and eat them up. One time in particular, Sarah got the first shot: She ate 1/4 of the Skittles. I went next, and I ate 1/9 of the ones on the floor. Sarah then let out a shriek and ate 1/3 of the remaining candies. I then ate 3/4 of the ones left. After Sarah ate 1/2 of the remaining Skittles, there were two yellow ones left, which we shared. How many Skittles did each of us eat?

Explanation / Answer

Let therer be x skittles

(1-.5)*(1-(3/4))(1- (1/3))*(8/9)*(x - x/4) = 2

.5*.25*(2/3)*(8/9)(3x/4) = 2
x = (2*3*9*4)/(2*1*3) = 36 in total

So, Sarah ate 1/4 of them first = 36/4 = 9
I ate 1/9 of reamining = 1/9 *(36-9) = 3

Sarah ate 1/3 of remaining or 24/3 = 8 by Sarah, and 16 were left
I ate 3/4 of that or 12 , leaving 4

Sarah ate away half of the skittles left i.e. 2 , leaving 4-2=2
Sarah and I shared the 1 each

So, Sarah had = 9+8+2+1= 20 skittles
I had = 3+12+1 = 16 skittles

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