Multiple choice

In a community sports event, there are 60 participants comprising athletes and coaches. The average score of the athletes is 82 points, while the average score of the coaches is 90 points. If the overall average score of all participants is 84 points, what is the ratio of the number of athletes to the number of coaches in the event?

  1. 3 : 1

  2. 1 : 3

  3. 2 : 5

  4. 5 : 2
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A Correct answer
Explanation

Using the allegation method: (Athletes average 82, Coaches average 90, Total average 84). The difference between 90 and 84 is 6, and between 84 and 82 is 2. The ratio of athletes to coaches is 6:2, which simplifies to 3:1.

AI explanation

Using the method of alligation, write the athletes' average of 82 and the coaches' average of 90 on the left, and place the overall average of 84 in the middle. The ratio of the differences is (90 - 84) to (84 - 82), which is 6 to 2. This simplifies to a ratio of 3 to 1 for the number of athletes to coaches.

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