Twenty men, women and children earn twenty coins between them. Each man earns 3 coins, each woman 1.5 coins and each child 0.5 coin. How many men, women and children are there?

Answer

There are 2 men, 5 women and 13 children.

Let the number of men, women and children be m, w, and c respectively. Then the problem states that:

m + w + c = 20

3m + 1.5w + 0.5c = 20

Multiplying equation 2 by 2 gives:

6m + 3w + c = 40

Subtracting the above equation from the first equation gives:

5m + 2w = 20

The unique solution is m = 2, w = 5 and c = 13.