To the delight of the May family, it is cherry season once again. Since Mrs. May’s three children like to eat cherries, she gets a large bowl of them and puts it on the kitchen table. Next to the bowl, she leaves a note that says each of the children is allowed to take a third of the cherries.
Julia comes home first and eats four cherries directly from the bowl before she sees the note next to it. After eating the four cherries, she takes a third of the remaining cherries. Tom, the second child to come home, believes that he is the first of his siblings to take cherries from the bowl. He first takes a single cherry and then a third of the remaining cherries. Fiona returns home last, but also thinks she is the first to arrive. She first takes two cherries and then a third of the cherries that remain. When Mrs. May returns home in the evening, she wonders why only 48 of the cherries were eaten.
How many cherries were in the bowl to begin with?
x represents the original number of cherries.
Julia leaves 2/3 * (x - 4) cherries.
Tom leaves 2/3 * (2/3 * (x - 4) - 1) cherries.
Since there are only 48 cherries left at the end, x - 48 cherries remain in the bowl after Fiona.
Thus, there were originally 64 cherries in the bowl.
Julia ate 24, Tom 14, and Fiona 10 cherries.