Random Puzzles 

Workings

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

Answer
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.

Workings

Hint
The answer is in the question.

Answer
Wrong.

Workings

Hint
You have to highlight three numbers.

Answer
2 + 13 + 2 = 17.

The puzzle didn't ask for three digits to be highlighted!

Workings

Hint
As we don't know how of the people were library members, you can try a random number and see what happens.

Answer
4,200 books.

Reasoning
It doesn't matter how many library members there were, as ¹/₂ of them accepted the books, and each accepted 6 books, which is 3 books per member on average.

Similarly, it doesn't matter how many non-members there were as ³/₄ of them accepted the books, and each accepted 4 books, which is again 3 books per non-member on average.

Double-Checking
Both the members and non-members accepted, on average, 3 books each.

And 1400 x 3 = 4200.