Here are the step-by-step solutions for each question on the worksheet.
1. How many books are available for loan?
*
Step 1: Identify which books can be borrowed. The problem says all books *except* reference books are available. This means we need to add the non-fiction and fiction books together.
*
Step 2: Add the number of non-fiction books (3,489) and fiction books (8,617).
$$3,489 + 8,617 = 12,106$$
*
Answer: There are
12,106 books available for loan.
2. How many reference books are on the shelf?
*
Step 1: Find the total number of reference books. The introduction states there are
1,240 reference books.
*
Step 2: Find out how many books are *not* on the shelf.
* Books in use: 128
* Books in the collection box: 84
* Total not on shelf: $128 + 84 = 212$
*
Step 3: Subtract the books that are not on the shelf from the total number of reference books to find how many are left on the shelf.
$$1,240 - 212 = 1,028$$
*
Answer: There are
1,028 reference books on the shelf.
3. How many patrons are there?
*
Step 1: We know the total money collected is $\$20,304$ and each patron pays $\$36$.
*
Step 2: To find the number of people, divide the total amount by the cost per person.
$$20,304 \div 36 = 564$$
*
Answer: There are
564 patrons.
4. How many books are left in the library?
*
Step 1: Calculate the total number of books in the library originally.
$$3,489 \text{ (non-fiction)} + 8,617 \text{ (fiction)} + 1,240 \text{ (reference)} = 13,346 \text{ total books}$$
*
Step 2: Calculate how many books have been borrowed. From Question 3, we know there are 564 patrons. Each patron has 6 books.
$$564 \times 6 = 3,384 \text{ books borrowed}$$
*
Step 3: Subtract the borrowed books from the total books to see what is left inside the library.
$$13,346 - 3,384 = 9,962$$
*
Answer: There are
9,962 books left in the library.
5. What is the maximum number of days a patron can keep the books?
*
Step 1: The initial loan is for
2 weeks. Since there are 7 days in a week, that is $2 \times 7 = 14$ days.
*
Step 2: The patron can renew the loan
twice. Each renewal adds another 2 weeks (14 days).
* First renewal: $+14$ days
* Second renewal: $+14$ days
*
Step 3: Add them all up: $14 + 14 + 14 = 42$ days.
*
Answer: The maximum number of days is
42.
6. Write an equation using "x" and then solve it.
*
Step 1: Determine the cost for one single book. The fee is $\$2$ per day for 9 days.
$$2 \times 9 = \$18 \text{ per book}$$
*
Step 2: Set up the equation. Let $x$ be the number of books. The total paid was $\$72$.
Equation:
$18x = 72$ (or $2 \cdot 9 \cdot x = 72$)
*
Step 3: Solve for $x$ by dividing both sides by 18.
$$x = 72 \div 18$$
$$x = 4$$
*
Answer: The equation is
$18x = 72$ and the solution is
$x = 4$.
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Final Answer:
1. 12,106
2. 1,028
3. 564
4. 9,962
5. 42
6. Equation: $18x = 72$; Solution: $x = 4$
Parent Tip: Review the logic above to help your child master the concept of division and multiplication worksheets.
