In a class with twice as many boys as girls, if the girls average 90 and the overall average is 80, what is the boys' average?

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Multiple Choice

In a class with twice as many boys as girls, if the girls average 90 and the overall average is 80, what is the boys' average?

Explanation:
This uses weighted averages with unequal group sizes. If there are g girls and twice as many boys, there are 2g boys. The girls contribute 90 per girl, so their total is 90g. The overall average is 80 for 3g students, giving a total of 80×3g = 240g for everyone. Subtract the girls’ contribution to find the boys’ total: 240g − 90g = 150g. Divide that by the number of boys (2g) to get the boys’ average: (150g)/(2g) = 75. So the boys’ average is seventy-five. (Quick check: (90g + 75×2g) / 3g = 240g/3g = 80, as given.)

This uses weighted averages with unequal group sizes. If there are g girls and twice as many boys, there are 2g boys. The girls contribute 90 per girl, so their total is 90g. The overall average is 80 for 3g students, giving a total of 80×3g = 240g for everyone. Subtract the girls’ contribution to find the boys’ total: 240g − 90g = 150g. Divide that by the number of boys (2g) to get the boys’ average: (150g)/(2g) = 75.

So the boys’ average is seventy-five. (Quick check: (90g + 75×2g) / 3g = 240g/3g = 80, as given.)

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