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?

Guest Apr 12, 2020

#1**0 **

Working backwards -- there were 7 left over.

Charles ate one extra cherry; putting it back, there were 8 cherries.

He ate 5/6^{ths} of the cherries; so the 8 represents 1/6^{th} 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 2/3^{rds} 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.

geno3141 Apr 12, 2020