My sister Lilly and I used to have a great time playing with

My sister, Lilly, and I used to have a great time playing with jelly beans. First we would place them in groups on the living room floor. Then we would pretend they were rabbits and we were hawks. We would swoop down and eat them up. Once time in particular, Lilly got the first shoot. She ate one-fifth of the jelly bean. I went next and I ate one-sixth of the jelly beans on the floor. Lilly then let out a shriek and ate two-fifths of the remaining beans. I then ate two-thirds of the ones left. After Lilly ate one-half of the remainning jelly beans, there were two yellow beans left, which we shared. How many jelly beans did each of us eat?

Solution

For this kind of problem, you have to work backwards. Since you ended up with two, right after Lilly ate 1/2 of the beans, multiply by its reciprocal 2. 2x2=4 To get four, you ate 2/3 of what you had before, which means 1/3 (1-2/3) were left. So multiply 4 by 3. 4x3=12 To get to those 12, Lilly had just eaten 2/5 of the remaining beans, therefore 3/5 (1-2/5) were left. 12x(5/3)= 20 To get to those 20, You ate 1/6, leaving 5/6 of the jelly beans there. 20x(6/5)=24 And finally to get to those 24, Lilly ate 1/5, leaving 4/5. 24x(5/4)=30

This gives that you ate 4+8+1 and Lilly ate 6+8+2 +1
So, all together, you ate 13 and Lilly ate 17, starting with a total of 30 and ending with 0.