Question

Kara owns 35 books. Of these books, 20% have fewer- than 100 pages and 80% have 100 pages or more. Complete the statement about the books Kara owns.

Kara owns blank books fewer than 100 pages and blank books with 100 pages or more.

Answer 1

explain why this is the answer

Answer 2

To find the number of books Kara owns that have fewer than 100 pages and those with 100 pages or more, we can use the percentages given.

1. Calculate the number of books with fewer than 100 pages:
\[
20\% \text{ of } 35 = 0.20 \times 35 = 7
\]

2. Calculate the number of books with 100 pages or more:
\[
80\% \text{ of } 35 = 0.80 \times 35 = 28
\]

Now we can complete the statement:

Kara owns **7** books fewer than 100 pages and **28** books with 100 pages or more.

Answer 3

To understand why the calculated numbers of books are correct, let's break down the problem step-by-step:

1. **Total Books**: Kara owns a total of **35 books**.

2. **Percentage Calculation**: The problem provides us with the percentages of books based on their page counts:
- **20%** of the books have fewer than 100 pages.
- **80%** of the books have 100 pages or more.

3. **Calculating the Number of Books with Fewer Than 100 Pages**:
- To find how many books correspond to 20% of the total, you multiply the total number of books (35) by 0.20 (which is 20% expressed as a decimal).
\[
0.20 \times 35 = 7
\]
This tells us that **7 books** have fewer than 100 pages.

4. **Calculating the Number of Books with 100 Pages or More**:
- For the books with 100 pages or more, you do the same thing using the percentage of 80%. This can also be confirmed by calculating 80% of the total books.
\[
0.80 \times 35 = 28
\]
This tells us that **28 books** have 100 pages or more.

5. **Verification of Percentages**:
- The sum of books should equal the total number of books:
\[
7 \text{ (fewer than 100 pages)} + 28 \text{ (100 pages or more)} = 35 \text{ (total books)}
\]
This confirms that our calculations are internally consistent.

Thus, the answer is valid and correctly describes the number of books Kara owns based on the provided percentages. So, Kara owns **7 books** with fewer than 100 pages and **28 books** with 100 pages or more.