The mean weight of 150 students in a certain class is 60kg. The mean weight of boys in the class is 70kg and that of the girls is 55kg. Find the number of boys and the number of girls in the class.
To find the number of boys and girls in the class, let's solve this problem step by step.
Let's assume the number of boys in the class is "b" and the number of girls is "g."
We're given that the mean weight of 150 students in the class is 60kg. This means the sum of all their weights is (150 * 60) kg.
We're also given that the mean weight of boys in the class is 70kg. This means the sum of the weights of all the boys is (b * 70) kg.
Similarly, the mean weight of girls in the class is 55kg. This means the sum of the weights of all the girls is (g * 55) kg.
Since the total number of students is 150, we can write an equation for the total weight:
(b * 70) + (g * 55) = (150 * 60)
Now, we have two unknowns, "b" and "g," but we have only one equation. To solve these types of problems, we usually need a second equation.
Since we don't have any other given information directly, we can see that the number of boys and girls should add up to the total number of students, 150.
So, we have a second equation:
b + g = 150
Now we have a system of equations:
(b * 70) + (g * 55) = (150 * 60) (Equation 1)
b + g = 150 (Equation 2)
We can now solve this system of equations to find the values of "b" and "g."
One way to solve it is to solve Equation 2 for "b" and substitute it into Equation 1:
b = 150 - g
Substituting this into Equation 1:
((150 - g) * 70) + (g * 55) = (150 * 60)
Now we have a single equation with one unknown (g) that we can solve:
(10500 - 70g) + 55g = 9000
10500 - 15g = 9000
-15g = -1500
g = 100
Now, substitute the value of "g" back into Equation 2 to find "b":
b + 100 = 150
b = 150 - 100
b = 50
Therefore, there are 50 boys and 100 girls in the class.