Read the riddle carefully and then answer the question.
20 people worked and earned $20 between them.
The workers include men, women and children.
If each man earns $ 3, each woman $1.50 and each child earns $ 0.50.
How many men, women and children are there?
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Answer: There are 2 men, 5 women and 13 children.
Let the number of men, women and children be m, w, and c respectively.
From the given information we can write the following 2 equations;
m + w + c = 20 ————-(1)
3m + 1.5w + 0.5c = 20 —–(2)
Multiplying equation (2) by 2 we get;
6m + 3w + c = 40 ———(3)
Subtracting (3) from the first equation we get;
5m + 2w = 20
The unique solution with whole numbers is m = 2 & w = 5
Therefore from equation(1) we can find;
c = 13.