Chestnut distribution

This riddle goes from three small chestnut search engines who decided to share the loot in proportion to their age. It is a very beautiful problem, which will surprise the very duo in mathematics. These little ones had never dedicated a second to mathematical arithmetic. They had not even bothered to count the number of chestnuts they had collected, 770.

They simply divided them according to their age. So every time Mary took 4, Nellie took 3, and for every 6 that Mary received Susie.

The problem consists in saying how many chestnuts each received and how ages they had.

Nellie, who was 4 and a half years old took 198, Mary, 6, took 264, and Susie, 7, took 308.

The problem analysis leads us to:

As Susie takes 7 per 6 of Mary and Nellie, she takes 3 out of 4 from Marie, she would take only 4 1/2 in each division of 4, 5, 6 and 7 that adds 17 1/2. So dividing 770 by 17.5 we have 44, which is the number by which we will multiply the ages.