There are 40 students in a class whose average weight is 56. 25kg.Among these 40 students 25 are boys and 15 are girls. The average weight of 25 boys is 6.8 kg more than the average weight of 15 girls. What is the average weight of 15 girls?
Question
There are 40 students in a class whose average weight is 56. 25kg.Among these 40 students 25 are boys and 15 are girls. The average weight of 25 boys is 6.8 kg more than the average weight of 15 girls. What is the average weight of 15 girls?
Solution
Let's solve this step by step:
Step 1: The total weight of all the students in the class is 40 (students) * 56.25 (average weight) = 2250 kg.
Step 2: Let's denote the average weight of the girls as 'x'. Therefore, the average weight of the boys is 'x + 6.8'.
Step 3: The total weight of the girls is 15 (girls) * x (average weight) and the total weight of the boys is 25 (boys) * (x + 6.8).
Step 4: Since the total weight of all the students is the sum of the total weight of the girls and the boys, we can set up the following equation: 15x + 25(x + 6.8) = 2250.
Step 5: Simplify the equation to get: 15x + 25x + 170 = 2250.
Step 6: Combine like terms to get: 40x + 170 = 2250.
Step 7: Subtract 170 from both sides to get: 40x = 2080.
Step 8: Divide both sides by 40 to solve for 'x': x = 52 kg.
Therefore, the average weight of the 15 girls is 52 kg.
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