Multiple choice

On a particular exam, the boys in a history class averaged $86$ points and the girls in the class averaged $80$ points. lf the overall class average was $82$ points, what was the ratio of boys to girls in the class?

  1. $2:1$
  2. $3:4$
  3. $4:3$.
  4. $1:2$.
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D Correct answer
Explanation

Let B be number of boys and G be number of girls. (86B + 80G) / (B + G) = 82. 86B + 80G = 82B + 82G. 4B = 2G. B/G = 2/4 = 1/2.

AI explanation

Using the method of alligation, the ratio of boys to girls is proportional to the difference between the girls average and the overall average compared to the difference between the overall average and the boys average. The differences are 82 minus 80, giving 2, and 86 minus 82, giving 4. This establishes a ratio of 2 to 4, which simplifies to 1:2.

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