Multiplication And Division Review Worksheets | 99Worksheets - Free Printable

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 compute:
$$
20,304 ÷ 36 = ?
$$

Break it down:
- 36 × 500 = 18,000
- Subtract: 20,304 − 18,000 = 2,304
- 36 × 60 = 2,160
- Subtract: 2,304 − 2,160 = 144
- 36 × 4 = 144

So: 500 + 60 + 4 = 564

✔ 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:
$$
\text{Books borrowed} = 564 × 6 = 3,384
$$

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

Now subtract borrowed books:
$$
\text{Books left} = 13,346 - 3,384 = 9,962
$$

✔ 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 can a patron keep the books he borrowed from the library?

#### Solution:
- Initial loan period: 2 weeks = 14 days
- Can renew twice, so 2 additional renewals
- Each renewal adds another 14 days

So total time:
$$
= 14 + 14 + 14 = 42 \text{ days}
$$

✔ 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:
Let’s define:
- Late fee per day per book = $2
- Number of books = x
- Overdue days = 9
- Total late fee = $72

So, total fee = (number of books) × (days overdue) × (fee per day)

$$
2 × x × 9 = 72
$$

Simplify:
$$
18x = 72
$$

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

✔ Answer: The equation is:
$$
18x = 72
$$
Solving: $ x = 4 $
So, the patron had 4 books overdue.

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✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1 | 12,106 books available for loan |
| 2 | 1,028 reference books on the shelf |
| 3 | 564 patrons |
| 4 | 9,962 books left in the library |
| 5 | 42 days maximum |
| 6 | Equation: $18x = 72$, Solution: $x = 4$ |

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