algebra

Joy is planning a party. One game she decides to play is bobbing for apples. She divides her apples into three amounts, thinking that putting a different number in each same-sized bucket might make ti more fun. Three friends are helping her. Joy puts 1/2 of her apples plus 1/2 apple into Becky's bucket. She then puts 1/2 of the remaining apples plus 1/2 into Gayle's bucker. She then puts 1/2 of the remaining apples plus 1/2 apple into Bonnie's bucket. One apple is left over, which Joy eats. How many apples did she start with? How many apples went into each helper's bucket?

asked by Alisha
  1. original amount: x apples
    Becky gets (x+1)/2, leaving Joy (x-1)/2
    Gayle gets (x+1)/4, leaving Joy (x-3)/4
    Bonnie gets (x+1)/8, leaving 1 left over

    x - (x+1)/2 - (x+1)/4 - (x+1)/8 = 1
    x = 15

    or, working backwards, there were

    ((1*2+1)*2+1)*2+1 = 15 apples to start

    posted by Steve

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