Solving for the Total Weight of Girls in a Group Based on Average Weights

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In any group of boys and girls, we often need to find the total weight of girls based on given average weights. Let's dive into a detailed exploration using algebraic methods to find the total weight of girls in a group where we know the total average weight, the number of boys, and the average weight of boys and girls.

Given Data and Notations

To make the problem more concrete, let's introduce some notations and data points:

b - number of boys wb - weight of each individual boy g - number of girls wg - weight of each individual girl Average weight of the group - 37.5 kg Average weight of the boys - 40 kg Average weight of the girls - 35 kg Number of boys - 25

Algebraic Setup

Let's set up the algebraic relations to solve for the variables.

The total weight of the boys can be expressed as bwb, and since we know the average weight of the boys is 40 kg, the total weight of the boys can be written as bwb 40b. The total weight of the girls is gwg. Since we know the total average weight of the group is 37.5 kg, the total weight of the group is total weight 37.5(b g).

Solving for the Number of Girls and the Total Weights

Substituting the known values into the equation, we get:

(25wb Wg) / (25 g) 37.5 kg.

Where Wg is the total weight of the girls. Given wb 40 kg and the average weight of the girls is 35 kg, we can rewrite the equation as:

(25 * 40 Wg) / (25 g) 37.5.

Given that the number of girls is 25, we can denote the total weight of the girls Wg 25 * 35. Let's simplify and solve for Wg:

(25 * 40 Wg) / (25 25) 37.5.

Which simplifies to:

(1000 Wg) / 50 37.5.

Then we solve for Wg by multiplying both sides by 50:

1000 Wg 1875.

Solving for Wg:

Wg 875 kg.

Conclusion

The total weight of the girls in this group, based on the given average weights, is 875 kg. This approach can be used to solve similar problems related to the average weights of mixed groups.

Key Points

The total weight of the group includes the weights of both boys and girls. Using the average weights, we can set up a balanced equation to find the total weights of each subgroup. This method can be applied to various real-world scenarios involving mixed group averages.

Understanding these algebraic methods can help in various fields, including demographic analysis, sports science, and health studies. By breaking down the problem into simpler equations, we can accurately determine the total weights of different subgroups within a larger group.