Here are the step-by-step solutions for the problems on the worksheet.
Problem 1
Question: All books, except the reference books, are available for loan. How many books are available for loan?
Step-by-step Solution:
1. Identify the types of books that can be borrowed: Non-fiction and Fiction. Reference books cannot be borrowed.
2. Find the number of non-fiction books:
3,489.
3. Find the number of fiction books:
8,617.
4. Add these two numbers together to find the total available for loan.
$$3,489 + 8,617 = 12,106$$
Answer for #1: 12,106 books
---
Problem 2
Question: If 128 reference books are in use and 84 reference books are in the collection box, how many reference books are on the shelf?
Step-by-step Solution:
1. Find the total number of reference books in the library:
1,240 (given at the top of the page).
2. Identify where the other books are:
* In use:
128
* In the collection box:
84
3. First, add the books that are *not* on the shelf to see how many are missing from it.
$$128 + 84 = 212$$
4. Subtract the missing books from the total number of reference books to find out how many are left on the shelf.
$$1,240 - 212 = 1,028$$
Answer for #2: 1,028 books
---
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?
Step-by-step Solution:
1. Identify the total amount of money collected:
$20,304.
2. Identify the cost per person (patron):
$36.
3. To find the number of people, divide the total money by the cost per person.
$$20,304 \div 36$$
*Calculation:*
* $203 \div 36 = 5$ (with a remainder of 23)
* Bring down the 0 to make 230.
* $230 \div 36 = 6$ (with a remainder of 14)
* Bring down the 4 to make 144.
* $144 \div 36 = 4$
The result is
564.
Answer for #3: 564 patrons
──────────────────────────────────────
Final Answer:
1. 12,106
2. 1,028
3. 564
Parent Tip: Review the logic above to help your child master the concept of mixed word problems.
