S bought 4 pens and 3 books. Each pen costs half of one book. The total cost of the items is $8. What is the cost for one pen?

Let the cost of one book be denoted as $ x $, and since each pen costs half of a book, the cost of one pen is $ \frac{x}{2} $.

Given that S bought 4 pens and 3 books, we can set up the total cost equation:

\[
4 \times \frac{x}{2} + 3x = 8
\]

Simplifying the first term:

\[
2x + 3x = 8
\]

Now combine like terms:

\[
5x = 8
\]

Solve for $ x $:

\[
x = \frac{8}{5} = 1.6
\]

Now that we know the cost of one book is $ 1.6 $ dollars, the cost of one pen is:

\[
\frac{x}{2} = \frac{1.6}{2} = 0.8
\]

Thus, the cost of one pen is **$0.80**.

Would you like further details or have any questions?

Here are some related questions to extend your understanding:
1. What would be the total cost if S bought 5 pens and 4 books?
2. If each pen cost $0.80, how many pens can S buy with $12?
3. What is the total cost if S bought 6 pens and 2 books?
4. If the cost of each pen increased by 20%, what would the new cost be?
5. How would the total cost change if S received a 10% discount on the books?

**Tip**: When solving word problems, assigning variables to unknown quantities and translating conditions into equations helps simplify the process.

This problem involves solving a linear equation to find the cost of one pen. S bought 4 pens and 3 books, with the total cost being $8. Learn how to set up and solve the equation using basic algebraic techniques, suitable for students in Grades 6-8.

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