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Puzzle - Answer

Three teachers were discussing how long they had been teaching.

Adrian and Betty had been teaching for a total of 36 years.

Charlie and Betty had been teaching for a total of 22 years.

Charlie and Adrian had been teaching for a total of 28 years.

How long had each been teaching?

 [Ref: ZKLD] © Kevin Stone

Answer:
Adrian had been teaching 21 years.
Betty had been teaching 15 years.
Charlie had been teaching 7 years.

Adrian and Betty had been teaching for a total of 36 years.

Charlie and Betty had been teaching for a total of 22 years.

Charlie and Adrian had been teaching for a total of 28 years.

Let Adrian = A, Betty = B and Charlie = C, then:

   A + B = 36       [1]
   C + B = 22       [2]
   C + A = 28       [3]

If we use [3] - [2] we have:

   A - B = 6        [4]

If we use [1] + [4] we have:

   2A = 42
    A = 21

By [1] B = 15. By [3] C = 7. QED.

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