Multiple choice

One adult and $10$ children are in an elevator. If the adult's weight is $4$ times the average (arithmetic mean) weight of the children, then the adult's weight is what fraction of the total weight of the $11$ people in the elevator?

  1. $\dfrac{2}{7}$
  2. $\dfrac{3}{7}$
  3. $\dfrac{4}{7}$

  4. None of the above
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A Correct answer
Explanation

Let A be the adult's weight and C be the average weight of the 10 children. A = 4C. Total weight of children = 10C. Total weight of all 11 people = A + 10C = 4C + 10C = 14C. Adult's fraction = A / (A + 10C) = 4C / 14C = 4/14 = 2/7.

AI explanation

Let the average weight of the 10 children be w, making the total weight of the children 10w. The adult's weight is given as 4 times w, so the total weight of all 11 people is 10w plus 4w, which is 14w. The adult's weight as a fraction of the total weight is 4w divided by 14w, which simplifies to 2/7.

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