Andrew, Bernard and Cathy shared a box of cupcakes. Andrew received 2/5 of the box of cupcakes and 2/5 of a cupcake. Bernard received 2/5 of the remaining box of cupcakes and 3/5 of a cupcake. If there was only 6 cupcakes left for Cathy, how many cupcakes were in the box at first?
Let the number of cupcakes in the box==C
Andrew gets==2/5C + 2/5 ==[2C + 2] / 5
C - [2C + 2] / 5 ==[3C - 2] / 5 - cupcakes left in the box.
Bernard receives==2/5 x [3C - 2]/5 + 3/5==[6C + 11] / 25.
[3C - 2]/5 - [6C + 11]/25==[9C - 21]/25 - cupcakes remain in box.
[9C - 21] / 25 ==6, solve for C
C ==19 cupcakes - original number in the box.
Andrew gets 8 cupcakes. Bernard gets 5 cupcakes. Cathy get the last 6 cupcakes.
