Multiple choice

In a middle school there were initially 12 teachers. If three teachers with ages 32 years, 34 years and 40 years left the school, the average age of the rest of the teachers reduced by 3. What was the average age(in years) of 12 teachers?

  1. 79/3

  2. 133/3

  3. 127/3

  4. 145/3

  5. None of these
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A Correct answer
Explanation

Let the average age of 12 teachers be A. Total age = 12A. After 3 teachers (32, 34, 40) leave, total age = 12A - 106. New average = (12A - 106) / 9 = A - 3. 12A - 106 = 9A - 27. 3A = 79. A = 79/3.

AI explanation

Let the initial average age of the 12 teachers be x, making their total age 12x. The three teachers who left have a total age of 32 + 34 + 40 = 106 years, leaving 9 teachers with a total age of 12x - 106. The new average age is x - 3, so the new total age can also be written as 9(x - 3), which gives the equation 12x - 106 = 9x - 27. Solving for x gives 3x = 79, so the initial average age was 79/3.

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