Question

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?

Answer 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