To solve this question, the user needs to know basic arithmetic and the concept of division. The user must divide the 20 pieces of bread among the given constraints of men, women, and children, and then check if the distribution satisfies the given conditions.
Let's calculate the total number of pieces eaten by each group:
- A man eats 3 pieces, so 1 man eats 3 pieces.
- A woman eats 2 pieces, so n women eat 2n pieces.
- A child eats half a piece, so m children eat 0.5m = m/2 pieces.
The total number of pieces eaten is:
3 + 2n + m/2
We want this to be equal to the total number of pieces of bread, which is 20. So we have:
3 + 2n + m/2 = 20
Multiplying both sides by 2, we get:
6 + 4n + m = 40
Subtracting 6 from both sides, we get:
4n + m = 34
We know that there are 20 people in total. Let's substitute the value of m in terms of n into this equation:
4n + m = 34
4n + 2m/2 = 34
4n + 2m = 68
2n + m = 34
m = 34 - 2n
Substituting this value of m in terms of n into the equation we got earlier:
3 + 2n + m/2 = 20
3 + 2n + (34 - 2n)/2 = 20
3 + 2n + 17 - n = 20
n = 5
So there are 5 women. Substituting this value of n into the equation we got earlier:
4n + m = 34
4(5) + m = 34
m = 14
So there are 14 children. And from the equation:
3 + 2n + m/2 = 20
3 + 2(5) + 14/2 = 20
So there is 1 man. Therefore, the correct option is:
The Answer is: A. There are 5 women, 1 man and 14 children.