2016 AIME II Problems/Problem 1
Initially Alex, Betty, and Charlie had a total of 
peanuts. Charlie had the most peanuts, and Alex had the least. The three numbers of peanuts that each person had formed a geometric progression. Alex eats 
of his peanuts, Betty eats 
of her peanuts, and Charlie eats 
of his peanuts. Now the three numbers of peanuts each person has forms an arithmetic progression. Find the number of peanuts Alex had initially.
