Correct Answer: 13 and 27
Explanation:
Given:
Let number of boys = x, number of girls = y
Use the weighted average formula:
(30x + 20y) / (x + y) = 23.25
Multiply both sides by (x + y):
30x + 20y = 23.25(x + y)
Eliminate decimals:
=> 30x + 20y = (93/4)(x + y) => Multiply both sides by 4: 120x + 80y = 93(x + y)
Now expand the right-hand side:
120x + 80y = 93x + 93y => 120x - 93x = 93y - 80y => 27x = 13y => x/y = 13/27
Therefore, possible strength of boys and girls =
13 boys and 27 girls (or any multiple of this ratio).
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