In a class, the average score of girls in an examination is 80, and the average score of boys is 90. If the average score of the whole class is 87, find the percentage of boys in the class.
Question
In a class, the average score of girls in an examination is 80, and the average score of boys is 90. If the average score of the whole class is 87, find the percentage of boys in the class.
Solution
To solve this problem, we can use the concept of weighted averages. Here are the steps:
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Let's denote the percentage of boys in the class as B and the percentage of girls as G. Since percentages must add up to 100%, we have B + G = 100%.
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We know that the average score of the whole class is a weighted average of the boys' and girls' average scores, with the weights being the percentages of boys and girls in the class. So, we can write the equation: 80G + 90B = 87 * 100.
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Now we have a system of two equations, and we can solve it. From the first equation, we can express G as 100 - B and substitute it into the second equation: 80 * (100 - B) + 90B = 8700.
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Simplifying this equation gives us 2000 - 10B + 90B = 8700, or 80B = 6700, so B = 6700 / 80 = 83.75.
So, the percentage of boys in the class is approximately 83.75%.
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