Mathematics

First task

The father originally decided to bequeathe the money on his two sons in such a way that they had to divide it in the ratio 8 : 7. Then he changed his decision  and divided the same sum in the ratio 11 : 9. This way, the value of the inheritance for the older son increased by 925 thalers. What amount did the father bequeathe on both sons together?

I. Solution

The original division is in the ratio 8 : 7, it means one part of the whole is by this division
 
from the inheritance.

The new division is in the ratio 11 : 9, it means one part of the whole is by this division

from the inheritance.

The difference in the inheritance for the older son is 925 thalers which responds

from the whole, as
.

Therefore, the whole inheritance must have the value 60 . 925 thalers, i. e. 55000 thalers.

II. Solution

We describe the whole inheritance as x thalers.

The original division is in the ratio 8 : 7, the inheritance for the older son is

By the new division, it is in the ratio 11 : 9, the inheritance for the older son is

The difference between these inheritances is 925 thalers.

Therefore we make up the equation:

The father bequethed both of his sons together 55000 thalers.