The average mass of a group of children is 36kg. If 3/7 of the no. of children are girls and their average mass is 32 kg, find the average mass of the boys.
number of girls = 3x
number of boys = 4x
(check: total is 7x)
total weight of all children = 7x(36) = 252x
total weight of all the girls = 3x(32) = 96x
so the weight of all the boys = 252x-96x = 156x
average weight of boys = 156x/(4x) = 39 kg
Let's assume the total number of children in the group is "x".
Given that 3/7 of the total number of children are girls, we can write this as (3/7)x.
The average mass of the girls is given as 32 kg. Therefore, the total mass of all the girls can be calculated as (32 kg) * (3/7)x.
Similarly, the average mass of the boys can be calculated as the total mass of all children minus the total mass of the girls, divided by the number of boys.
The total mass of all children is given as 36 kg, and we know that the average mass of all the girls is (32 kg) * (3/7)x. Therefore, the total mass of the boys can be calculated as 36 kg - (32 kg) * (3/7)x.
Since we want to find the average mass of the boys, we divide the total mass of the boys by the number of boys, which is x - (3/7)x, or (4/7)x.
Therefore, the average mass of the boys can be calculated as:
[(36 kg) - (32 kg * (3/7)x)] / [(4/7)x]
To find the average mass of the boys, we need to first determine the number of girls and boys in the group.
Let's assume there are x children in the group. According to the information given, 3/7 of the total number of children are girls. So, the number of girls would be (3/7) * x.
The remaining number of children would then be (1 - 3/7) * x, which simplifies to (4/7) * x, representing the number of boys.
Now, let's calculate the total mass of the girls. Since the average mass of the girls is 32 kg, multiplying this by the number of girls will give us the total mass of the girls: (32 kg) * (3/7) * x.
Similarly, let's calculate the total mass of the boys. The total mass of the boys would be (36 kg * x) - [(32 kg) * (3/7) * x], as this calculation subtracts the total mass of the girls from the total mass of all the children.
Finally, to find the average mass of the boys, we divide the total mass of the boys by the number of boys, [(36 kg * x) - (32 kg * (3/7) * x)] / [(4/7) * x]. Simplifying this expression gives us the average mass of the boys.
Therefore, the average mass of the boys is [(36 * x) - (32 * (3/7) * x)] / [(4/7) * x].