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The local library decided to hand out some of its old books to its 1400 borrowers.

To each of the female borrowers they gave 6 books and to each male borrower they gave 4 books.

If only half of the females in town and three quarters of the males in town accepted the books, how many books were given away?

It doesn't matter how many female borrowers there were as 1/2 of the females accepted the books, and those that did accepted 6 books, which is 3 books per female on average.

Similarly it doesn't matter how many male borrowers there were as 3/4 of the males accepted 4 books each, which is again 3 books each.

So both the males and females accepted, on average, 3 books each. And 1400 * 3 = 4200. QED.

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