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Three teachers were discussing how long they had been teaching.

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

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

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

How long had each been teaching?

Betty had been teaching 15 years.
Charles had been teaching 7 years.

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

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

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

Let Adrian = A, Betty = B and Charles = 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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