My local library decided to hand out some of its old books to the 1,400 people who lived in the town.

To each library member, they offered 6 books, and to each non-member, they offered 4 books.

If only half of the members, and three-quarters of the non-members, accepted the books, how many books were given away?

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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.