Question

From al-Khowarizmi's Algebra: Ten dinar is divided equally among a group of men so that when 6 more men are added to their number and 40 dinar is divided equally among them, then each receives as much as he did previously. Find the original number of men.

Answer 1

The original number of men is 2

Explanation:

Let the number of men be x

The amount each of the men will receive from the ten dinar since they all received equal amounts will be 10/x

Now, adding 6 more men, we have a total of x + 6 men now

Now we share 40 dinar amongst the x + 6 men and each will receive 10/x as received before

Mathematically;

40/x + 6 = 10/x

x(40) = 10(x + 6)

40x = 10x + 60

40x -10x = 60

30x = 60

x = 60/30

x = 2

There were originally 2 men