In a primary school the average weight of male students is 65.9 kgs and the average weight of female students is 57 kg.If the average weight of all the students is 60.3kg and the number of male students in the school is 66.What is the number of female students in the school?11411266None of these

To solve this problem, we can use the formula for the weighted average. The weighted average is given by (Sum of all weights) / (Total number of items). In this case, the weights are the average weights of the male and female students, and the items are the number of students.

We know that the average weight of all students is 60.3 kg, and the number of male students is 66. We can express the total weight of all students as:

Total weight = (Average weight of all students) * (Total number of students) Total weight = (Average weight of male students * Number of male students) + (Average weight of female students * Number of female students)

We can then solve for the number of female students:

Number of female students = (Total weight - (Average weight of male students * Number of male students)) / Average weight of female students

Substituting the given values:

Number of female students = (60.3 * Total number of students - 65.9 * 66) / 57

We don't know the total number of students yet, but we can express it in terms of the number of male students and female students:

Total number of students = Number of male students + Number of female students Total number of students = 66 + Number of female students

Substituting this into the equation gives:

Number of female students = (60.3 * (66 + Number of female students) - 65.9 * 66) / 57

This is a linear equation in the number of female students, which can be solved to find the number of female students.

To solve this problem, we can use the formula for the weighted average. The weighted average is given by (Sum of all weights) / (Total number of items). In this case, the weights are the average weights of the male and female students, and the items are the number of male and female students.

We know that the average weight of all students is 60.3 kg, and the number of male students is 66. Let's denote the number of female students as F.

We can set up the following equation:

(65.9 * 66 + 57 * F) / (66 + F) = 60.3

Solving this equation for F will give us the number of female students.

First, multiply both sides of the equation by (66 + F) to get rid of the denominator on the left side:

65.9 * 66 + 57 * F = 60.3 * (66 + F)

Next, distribute the 60.3 on the right side:

65.9 * 66 + 57 * F = 60.3 * 66 + 60.3 * F

Then, subtract 60.3 * 66 and 57 * F from both sides to isolate F:

(65.9 - 60.3) * 66 = (60.3 - 57) * F

Finally, divide both sides by (60.3 - 57) to solve for F:

F = (65.9 - 60.3) * 66 / (60.3 - 57)

Calculating the right side will give us the number of female students.