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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?

 Jun 18, 2022
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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.

 Jun 20, 2022

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