Mixed Operations Word Problems worksheet for students to solve math problems involving library books.

Let's solve each of the Mixed Operations Word Problems step by step and explain the reasoning.

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Given:

- Non-fiction books: 3,489
- Fiction books: 8,617
- Reference books: 1,240

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Problem 1:

All books, except the reference books, are available for loan. How many books are available for loan?

#### Solution:
We need to add non-fiction and fiction books (since only reference books are not available for loan).

$$
\text{Books available for loan} = \text{Non-fiction} + \text{Fiction}
$$
$$
= 3,489 + 8,617 = 12,106
$$

✔ Answer: 12,106 books are available for loan.

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Problem 2:

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:
Total reference books = 1,240
Books in use = 128
Books in collection box = 84

So, books on the shelf = Total − In use − In collection box

$$
= 1,240 - 128 - 84 = 1,028
$$

✔ Answer: 1,028 reference books are on the shelf.

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Problem 3:

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:
To find number of patrons, divide total collected by fee per patron:

$$
\text{Number of patrons} = \frac{20,304}{36}
$$

Let’s do the division:
$$
20,304 ÷ 36 = 564
$$

(You can verify: $ 36 × 564 = 20,304 $)

✔ Answer: There are 564 patrons.

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Problem 4:

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

#### Solution:
From Problem 3, we know there are 564 patrons.

Each is borrowing 6 books, so total books borrowed:
$$
564 × 6 = 3,384
$$

Total books in the library:
$$
\text{Non-fiction} + \text{Fiction} + \text{Reference} = 3,489 + 8,617 + 1,240 = 13,346
$$

Now, subtract borrowed books from total:
$$
13,346 - 3,384 = 9,962
$$

✔ Answer: 9,962 books are left in the library.

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Problem 5:

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

#### Solution:
- Initial loan period: 2 weeks = 14 days
- Can renew twice, so 2 renewals × 14 days = 28 days
- Total time = Original + 2 renewals

$$
14 + 14 + 14 = 42 \text{ days}
$$

✔ Answer: A patron can keep the books for a maximum of 42 days.

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Problem 6:

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:
- Late fee per book per day = $2
- Overdue for 9 days
- Number of books = $ x $

So, total late fee = $ x \times 2 \times 9 = 18x $

Set equal to $72:
$$
18x = 72
$$

Solve for $ x $:
$$
x = \frac{72}{18} = 4
$$

✔ Answer:
Equation: $ 18x = 72 $
Solution: $ x = 4 $
So, the patron had 4 books overdue.

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✔ Final Answers Summary:

1. 12,106 books are available for loan.
2. 1,028 reference books are on the shelf.
3. There are 564 patrons.
4. 9,962 books are left in the library.
5. Maximum 42 days.
6. Equation: $ 18x = 72 $ → $ x = 4 $

Let me know if you'd like this formatted as a printable answer sheet!