Genghis Khan organized his men into groups of 10 soldiers under a "leader of 10." Ten "leaders of 10" were under a "leader of 100." Ten "leaders of 100" were under a "leader of 1000." * (a) If Khan had an army of 10,000 soldiers at the lowest level, how many men in total were under him in his organization? (b) If Khan had an army of 5763 soldiers at the lowest level, how many men in total were under him in his organization? Assume that the groups of 10 should contain 10 if possible, but that one group at each level may need to contain fewer.

(a) 11110 soldiers

(b) 6404 soldiers

Step-by-step explanation:

Following that logic you can express the men of any level of his organization as 10^n, where n is the level. Some examples:

Level 1: 10^1 = 10

Level 2: 10^2 = 100 Each of the 10 men in level 1 are in charge of 10 men in the level 2 (10 * 10 = 100)

(a) if the lowerst level of the organization has 10,000 soldiers, then the lowest level is:

10^n = 10,000

n = 4

The total number of men under him is:

10^4+10^3+10^2+10^1 = 11110 (Assuming that he is the leader of the first 10 leaders)

(b) In this case the lowest level has 5763, you have a 1 leader for every 10 soldiers, then the leaders needed for the lowest level is:

5763 / 10 = 576.3 = 577 leaders

These 577 leaders also have their own leaders for every 10:

577/10 = 57.7 = 58 leaders

And these also have their own leaders:

58 / 10 = 5.8 = 6

And again We assume these 6 are directly under Genghis Khan

Total soldiers:

5763 + 577 + 58 + 6 = 6404 soldiers