Multiple choice

Three friends Sara, Wais and Alice have some candies. The numbers of candies eaten by Sara, Wais and Alice are a, b and c, respectively. The average number of candies they ate all together is 7a, where a ≠ 0. What is the ratio of the number of candies eaten by Sara to the sum of the numbers of candies eaten by Wais and Alice?

  1. 20 : 1

  2. 1 : 20

  3. 2 : 7

  4. 3 : 8

  5. 9 : 20
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B Correct answer
Explanation

Total candies = a + b + c. Average = (a+b+c)/3 = 7a. Thus, a+b+c = 21a, which means b+c = 20a. The ratio of a to (b+c) is a : 20a, which is 1 : 20.

AI explanation

The average number of candies eaten by the three friends is (a + b + c) / 3, and setting this equal to 7a gives the equation a + b + c = 21a. Simplifying this equation by subtracting a from both sides results in b + c = 20a. The ratio of the number of candies eaten by Sara, which is a, to the sum of the candies eaten by Wais and Alice, which is b + c, is therefore a to 20a, simplifying to 1 : 20.

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