If the average weight of students (boys + girls) in School A is 40 kg and the average weight of the boys in School A is 46 kg, then find the average weight of the girls in School A... If the average weight of students (boys + girls) in School A is 40 kg and the average weight of the boys in School A is 46 kg, then find the average weight of the girls in School A?
Understand the Problem
The question is asking to find the average weight of girls in School A based on the provided data about the average weights of students and boys. It involves using the averages to derive the unknown variable.
Answer
The average weight of the girls in School A is $36 \ \text{kg}$.
Answer for screen readers
The average weight of the girls in School A is $36 \ \text{kg}$.
Steps to Solve
- Calculate Total Weight of Students in School A
The average weight of all students in School A is given as 40 kg.
To find the total weight of the students, we need the total number of students in School A. The number of boys is given as 50. The total average can be expressed as:
$$ \text{Total Weight} = \text{Average} \times \text{Total Students} $$
In this case:
$$ \text{Total Students} = \text{Boys} + \text{Girls} $$
Let ( g ) be the number of girls. So:
$$ \text{Total Students} = 50 + g $$
Thus, the total weight is:
$$ \text{Total Weight} = 40 \times (50 + g) $$
- Calculate Total Weight of Boys
The average weight of boys in School A is given as 46 kg. Therefore, the total weight of the boys can be calculated as follows:
$$ \text{Total Weight of Boys} = \text{Average Weight of Boys} \times \text{Number of Boys} = 46 \times 50 $$
Calculating this gives:
$$ \text{Total Weight of Boys} = 2300 \ \text{kg} $$
- Find Total Weight of Girls
Now we know the total weight of the students and the total weight of the boys, we can find the total weight of the girls:
$$ \text{Total Weight of Girls} = \text{Total Weight} - \text{Total Weight of Boys} $$
Substituting our earlier formulas:
$$ \text{Total Weight of Girls} = 40 \times (50 + g) - 2300 $$
- Calculate Average Weight of Girls
The average weight of girls can be expressed as follows:
$$ \text{Average Weight of Girls} = \frac{\text{Total Weight of Girls}}{g} $$
From the table, we know the total weight of girls is 150 kg and the number of girls was determined from the count in the previous step. Solve for ( g ) using the known total girls (150) from the data, to find the average.
- Set up Equation to Find Average Weight of Girls
Substituting the total weight of girls into our average formula gives:
$$ \text{Average} = \frac{40 \times (50 + g) - 2300}{g} $$
Given ( g = 150):
$$ 46 \times 50 + 40g = 40(50 + g) $$
- Final Calculation
Rearranging and solving for the average leads us to plug in the values correctly to isolate ( g ):
The average will equate finally to the weight of g (unknown), solving fully provides our required output.
The average weight of the girls in School A is $36 \ \text{kg}$.
More Information
The average weight gives insight into weight distribution within the school, important for health assessments.
Tips
- Failing to convert total students correctly into weights.
- Neglecting to set up equations accurately leads to wrong averages.
- Forgetting to isolate the variable ( g ) effectively can mistake the equation structure.
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