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.