Mixed Operations Word Problems worksheet for students to solve library-related math scenarios.

Let's solve each problem step by step.

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Problem 1:

Question: A library has 3,489 non-fiction books, 8,617 fiction books, and 1,240 reference books. All books, except the reference books, are available for loan. How many books are available for loan?

Solution:
1. Total number of non-fiction books = 3,489
2. Total number of fiction books = 8,617
3. Total number of reference books = 1,240

Since only non-fiction and fiction books are available for loan:
- Books available for loan = Non-fiction books + Fiction books
- Books available for loan = 3,489 + 8,617 = 12,106

Answer: \(\boxed{12106}\)

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Problem 2:

Question: Reference books are for use in the library. There are 16 bookshelves for the reference books. After use, they need to be returned to a special collection box for shelving. If 128 reference books are in use and 84 reference books are in the collection box, how many reference books are on the shelf?

Solution:
1. Total number of reference books = 1,240
2. Number of reference books in use = 128
3. Number of reference books in the collection box = 84

The number of reference books on the shelf is the total number of reference books minus the books in use and in the collection box:
- Books on the shelf = Total reference books - Books in use - Books in the collection box
- Books on the shelf = 1,240 - 128 - 84 = 1,028

Answer: \(\boxed{1028}\)

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Problem 3:

Question: Each patron pays an annual fee of $36 to the library. If the library collects $20,304 from the annual fee, how many patrons are there?

Solution:
1. Annual fee per patron = $36
2. Total annual fee collected = $20,304

The number of patrons is the total annual fee collected divided by the annual fee per patron:
- Number of patrons = Total annual fee / Annual fee per patron
- Number of patrons = 20,304 / 36 = 564

Answer: \(\boxed{564}\)

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Problem 4:

Question: Each patron can borrow up to 6 books. If all the patrons are currently holding onto 6 books each, how many books are left in the library?

Solution:
1. Total number of patrons = 564 (from Problem 3)
2. Each patron borrows 6 books
3. Total number of books borrowed = Number of patrons × Books per patron
- Total books borrowed = 564 × 6 = 3,384

The total number of books in the library is the sum of non-fiction, fiction, and reference books:
- Total books in the library = 3,489 (non-fiction) + 8,617 (fiction) + 1,240 (reference) = 13,346

The number of books left in the library is the total number of books minus the books borrowed:
- Books left = Total books - Books borrowed
- Books left = 13,346 - 3,384 = 9,962

Answer: \(\boxed{9962}\)

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Problem 5:

Question: Each patron can borrow the books for 2 weeks and renew the loan twice. What is the maximum number of days can a patron keep the books he borrowed from the library?

Solution:
1. Initial loan period = 2 weeks = 14 days
2. Renewal period = 2 weeks = 14 days per renewal
3. Maximum renewals allowed = 2

The maximum number of days a patron can keep the books is the initial loan period plus two renewals:
- Maximum days = Initial loan + 2 × Renewal period
- Maximum days = 14 + 2 × 14 = 14 + 28 = 42

Answer: \(\boxed{42}\)

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Problem 6:

Question: Write an equation using "x" and then solve the equation. The late fee for each day is $2. A patron paid $72 for x books that are overdue for 9 days.

Solution:
1. Late fee per day = $2
2. Number of days overdue = 9
3. Total late fee paid = $72

The total late fee is the product of the number of books, the number of days overdue, and the late fee per day:
- Total late fee = Number of books × Number of days overdue × Late fee per day
- 72 = x × 9 × 2

Simplify the equation:
- 72 = 18x

Solve for \( x \):
- \( x = \frac{72}{18} = 4 \)

Answer: \(\boxed{4}\)

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Final Answers:

1. \(\boxed{12106}\)
2. \(\boxed{1028}\)
3. \(\boxed{564}\)
4. \(\boxed{9962}\)
5. \(\boxed{42}\)
6. \(\boxed{4}\)