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The problem asks for a formula that describes how much Denise spends at a book sale, given certain conditions:

- Denise pays a fixed admission cost of $5.
- She also pays a fixed cost for each book she buys.
  
The variables are:
- $ b $ = cost of each book,
- $ n $ = number of books she buys,
- $ t $ = total cost of attending the book sale.

To write a formula for the total cost $ t $, we consider the following:
- The fixed admission cost is $5, so this is always included.
- Denise also spends $ b \times n $ on books, where $ b $ is the cost per book, and $ n $ is the number of books she buys.

Thus, the formula for the total cost $ t $ is:

\[
t = 5 + b \times n
\]

Would you like further details or have any questions? Here are 5 related questions to deepen your understanding:

1. How would the formula change if there was no admission fee?
2. If Denise buys 3 books at $10 each, what would be the total cost?
3. What if the cost per book varies? How would you modify the formula?
4. Can you express $ b $ in terms of $ t $ if the number of books $ n $ and the total cost $ t $ are known?
5. How does the formula change if Denise gets a discount on the admission fee?

**Tip**: When working with word problems, clearly identify fixed costs versus variable costs to build the correct formula.

Denise attends a book sale at her local library each year. The library sells books it no longer wants at a discount to the public. She pays a fixed admission cost of $5, plus a fixed cost for each book she purchases. Write a formula that describes how much Denise spends at the book sale. Let's let b = cost of each book, n = number of books she buys, t = total cost of attending the book sale.

Learn how to create a linear equation to determine the total cost of attending a book sale with a fixed admission fee and variable book costs. Understand the use of variables and basic algebraic concepts. Suitable for students in Grades 6-8.

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