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      Question

      A school has 8 teachers and 4 administrators. The

      average age of the teachers is 40 years, and the average age of the administrators is 55 years. After hiring 3 new teachers and 2 new administrators, the average age of the entire staff increases by 1 year. If the average age of the new teachers is 42 years, what is the combined age of the 2 new administrators?
      A 102 years Correct Answer Incorrect Answer
      B 108 years Correct Answer Incorrect Answer
      C 112 years Correct Answer Incorrect Answer
      D 116 years Correct Answer Incorrect Answer
      E none Correct Answer Incorrect Answer

      Solution

      Let the total age of 2 new administrators be x years Total age of 8 teachers and 4 administrators = 8 × 40 + 4 × 55 = 540 Average age of school = 540/12 = 45 When 3 new teachers and 2 new administrators joined then total age = 17 × (45+1) = 782 total age of the new teachers and administrators combined = 782-540 = 242 years age of 3 teacher + age of 2 administrators = 242 3 × 42 + x = 242 x = 242-126 x = 116

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