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Workings

Hint

Answer
375 children: 70 mothers and 55 fathers.

Workings

Hint
My first letter is E.

Answer
Envelope.

From pole, love, pen, and eel.

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.

Workings

Hint
Where did Max finish?

Answer
   #1 Logan Green  18
   #2 Kelly Red    24
   #3 Max   Blue   28
   #4 Jesse Yellow 21

Reasoning
By (1), the 18-year-old won the championship.
By (3), Kelly finished second.
By (6), the person who came last was 21.
   #1              18
   #2 Kelly
   #3
   #4              21

By (4), Max was the oldest competitor at 28, and can only have finished third. Which means that Kelly must have been 24.
   #1              18
   #2 Kelly        24
   #3 Max          28
   #4              21

By (2), the person who wore Red can only be 21 or 24, so Max can't have worn Red. Max didn't wear Green (4), and didn't wear Yellow (5), so Max must have worn Blue.
   #1              18
   #2 Kelly        24
   #3 Max   Blue   28
   #4              21

By (5), Kelly didn't wear Yellow, and by (4) didn't wear Green, so must have worn Red.
   #1              18
   #2 Kelly Red    24
   #3 Max   Blue   28
   #4              21

By (2), Jesse was 21. Which means that Logan was 18.
   #1 Logan        18
   #2 Kelly Red    24
   #3 Max   Blue   28
   #4 Jesse        21

By (4), Logan wore Green. Which means that Jesse wore Yellow.
   #1 Logan Green  18
   #2 Kelly Red    24
   #3 Max   Blue   28
   #4 Jesse Yellow 21