A king died leaving his gold bars to his 6 sons.

Question

A king died, leaving his gold bars to his 6 sons. The youngest son received a certain number of gold bars. The second youngest received twice as many, the third youngest three times as many, and so on. The queen ordered each son to give 2 gold bars to every son younger than himself. If, after this, all the sons had the same number of gold bars, how many did each now have?

Answer 1

I like this problem!

 

So lets suppose the youngest son had x bars to start with,  Then the older sons had 2x, 3x, 4x, 5x, and 6x respectively.

 

After the re-distribution the youngest will now have x + 10 bars ( the plus 10 is 2 from each of 5 brothers).  The second youngest will have 2x + 6  (gained 8 from older, gave 2 to younger.  By the same logic the next older ones will have 3x + 2, 4x - 2, 5x - 6 and 6x - 10 respectively. (This is more than we need to know, but helps understand what's going on)

 

Since all of these are equal we can solve by using any two brothers amount of gold.    Taking the first two:

 x + 10 = 2x + 6

-x            -x              Subtract x from both sides

        10 = x + 6

         -6          -6        Subtract 6 from both sides

          4 = x   => x = 4

 

Remember, x is what the youngest originally had, so now he and all his brothers have x + 10 = 4 + 10 = 14 bars of gold