Three brothers stayed in a house with their mother. One day, their mother brought home some cherries.
Alex woke up first. As he was hungry, he ate 1/2 the cherries plus one extra cherry and headed out.
Brian woke up next. As he was hungry, he takes 1/3 of the remaining cherries along and after he ate, he put two cherry back in the basket.
Charles woke up next. As he was hungry, he ate 5/6 of the remaining plus one extra cherry and headed out.
Their mother came home and saw seven cherries in the basket. How many cherries were there initially?
+23246 Working backwards -- there were 7 left over.
Charles ate one extra cherry; putting it back, there were 8 cherries.
He ate 5/6ths of the cherries; so the 8 represents 1/6th of the cherries; 6 x 8 = 48 cherries.
Brian put 2 cherries back (I hope he put them back before he ate them!): 48 - 2 = 46 cherries.
This represents 2/3rds of the cherries: 46 x 3/2 = 69 cherries.
Alex ate one extra cherry: 69 + 1 = 70 cherries.
He ate 1/2 of the cherries: 70 x 2 = 140.
Checking:
Start with 140 cherries.
Alex: Eat 1/2 of them (70) plus one more -- leaving 69 cherries.
Brian: Eat 1/3 of them (23) but put 2 back -- leaving 48 cherries.
Charles: Eat 5/6 of them (40) plus one more -- leaving 7 cherries.
