Chris has some eggs to sell and Maria AiLing and Jermaine wa

Chris has some eggs to sell and Maria, Ai-Ling, and Jermaine want to buy them Chris sells half the eggs plus half an egg to Maria, then sells half the remaining eggs plus half an egg to Ai-Ling. and finally sells half the remaining eggs plus half an egg to Jermaine. At the end of the three sales, Chris is out of eggs. The strange thing is that Chris never had to break an egg. How many eggs did Chris begin with? (Given to third-grade students)

Solution

Let X be the number of eggs Chris has to start with. \"Chris sells half the eggs plus half an egg to Maria\". So he sells X/2+ 1/2= (X+ 1)/2 to Maria which leaves Chris with X- (X+1)/2= (X- 1)/2 eggs.

\"then sells half the remaining eggs plus half an egg to Ai-Ling\". So he sells ((X- 1)/2)/2+ 1/2= X/4- 1/4+ 1/2= (X+1)/4 eggs which leaves Chris with (X- 1)/2- (X+ 1)/4= X/2- X/4- 1/2- 1/4= (X- 3)/4 eggs.

\"and finally sells half the remaining eggs plus half an egg to Jermaine.\" So he sells ((X- 3)/4)/2+ 1/2 = X/8- 3/8+ 1/2= X/8+ 1/8= (X+ 1)/8 eggs which leaves Chris with (X- 3)/4- (X+1)/8= (X- 7)/8 eggs.

The number of eggs given each time are (X+ 1)/2, (X+ 1)/4, (X+ 1)/8 and the number of eggs he has left are (X- 1)/2, (X- 3)/4, (X- 7)/8.
After selling those eggs to 3 people, Chris has none left: he has sold all X of his eggs. (X- 7)/8= 0 so X=7