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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?

 Apr 12, 2020
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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.

 Apr 12, 2020

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