Solving for the Number of Boys and Girls Using Mean Weight

In a class of 200 students, the average weight is 70 kg. The mean weight of boys is 80 kg, and the mean weight of girls is 55 kg. Using this information, we can determine the number of boys and girls in the class through a system of equations. This solution will ensure accurate representation of the class composition.

Given Data and Initial Equations

Let's begin by defining our variables:

B is the number of boys. G is the number of girls.

The total number of students in the class is 200. Therefore, the relationship between the number of boys and girls can be expressed as:

B G 200 ... (1)

The total weight of the class is 14,000 kg (since 200 students × 70 kg average weight 14,000 kg).

For the boys, the mean weight is 80 kg, which can be represented as:

80B

The girls' mean weight is 55 kg, so their total weight is:

55G

Setting up the equation for the total weight in the class:

80B 55G 14000 ... (2)

Solving the Equations

Now, we can use equation (1) and (2) to solve for B and G.

From equation (1), we can express G as:

G 200 - B ... (3)

Substitute (3) into equation (2):

80B 55(200 - B) 14000

80B 11000 - 55B 14000

25B 3000

B 120

Using B 120 in equation (1) to find G:

G 200 - 120 80

Therefore, there are 120 boys and 80 girls in the class.

Alternative Method

For another method, we can reframe the problem as follows:

Let x be the number of boys and y be the number of girls.

Given:

Total students: x y 150 ... (4)

Average weight: (79x 55y) / 150 60

We can rearrange this equation as:

79x 55y 9000 ... (5)

From equation (4), we solve for y:

y 150 - x ... (6)

Substitute equation (6) into equation (5):

79x 55(150 - x) 9000

79x 8250 - 55x 9000

24x 750

x 31.25

Given that the number of boys must be an integer, we approximate x to 31, and y to 119.

Thus, we find that there are 31 boys and 119 girls in the class.

Conclusion

By using both algebraic methods and equations, we can accurately determine the number of boys and girls in a class based on the given mean weight data. This solution ensures that the class composition is correctly represented and can be applied to similar problems in the future.