# Puzzle ZKLD

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Three teachers were discussing how long they had been teaching.

Alex and Billie had been teaching for a total of 36 years.
Charlie and Billie had been teaching for a total of 22 years.
Charlie and Alex had been teaching for a total of 28 years.
How long had each been teaching?

Alex had been teaching for 21 years.
Billie had been teaching for 15 years.
Charlie had been teaching for 7 years.

Reasoning
If we look at all of the clues, each person appears exactly twice.

So the total of the three clues gives us two lots of Alex + Billie + Charlie = 36 + 22 + 28 = 86.

So, Alex + Billie + Charlie = 43 years.

In each clue we are given two of the people, so we can use this to find the missing person:

Charlie and Billie had been teaching for a total of 22 years, which means that Alex must be: 43 - 22 = 21 years.

Charlie and Alex had been teaching for a total of 28 years, which means that Billie must be: 43 - 28 = 15 years.

Alex and Billie had been teaching for a total of 36 years, which means that Charlie must be: 43 - 36 = 7 years.

Reasoning With Algebra
Let Alex = A, Billie = B and Charlie = C, then:

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

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

[4]   A - B = 6

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

2A = 42
A = 21

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

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