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Nanyang Library charges for borrowing books.
Answer: (1) Do I need to pay 20 yuan for the membership card?

(2) Library card: 50÷ 100= 0.5 yuan every day.

So borrow books with a book rental card and charge 0.5 yuan every day;

(3) It costs X yuan to rent books and get a membership card every day.

Then 20+ 100x=50,

The solution is x = 0.3.

So borrow books with a membership card and charge 0.3 yuan every day;

(4) When the book borrowing time is within one year 100 days, it is cost-effective to use the book borrowing card; When it exceeds 100 days, it is cost-effective to use a membership card; When it happens to be 100 day, the cost of choosing two cards is the same.