At a sale, old books are on sale at 50 cents each, or 3 for $1. What is the greatest number of old books that you can buy with $9.90?

To solve this problem, let's first break down the pricing and then determine the maximum number of books you can buy with $9.90.

### Step 1: Understanding the Pricing
- **50 cents each**: If you buy one book, it costs $0.50.
- **3 for $1**: If you buy three books together, it costs $1. This is a better deal than buying each book individually.

### Step 2: Calculate the Number of Books with the Best Deal
- With the "3 for $1" deal, you get 3 books for $1. 
- Now, we need to determine how many full sets of 3 books you can buy with $9.90.

Divide $9.90 by $1:

\[
\frac{9.90}{1} = 9.90
\]

Since each dollar allows you to buy 3 books, multiply 9.90 by 3:

\[
9.90 \times 3 = 29.7
\]

You can purchase 29 full sets of books using this deal, giving you:

\[
\text{Number of books} = 29 \times 3 = 87 \text{ books}
\]

However, 29 full sets of 3 would cost exactly $9.90, meaning no money is left over to buy any more books individually.

### Conclusion
The greatest number of old books you can buy with $9.90 is **87 books**.

Would you like more details or have any other questions?

Here are some related questions:

1. What if the budget was $10? How many books could you buy then?
2. How much would it cost to buy 100 books using this deal?
3. What is the maximum number of books you can buy with $5?
4. If the deal was changed to "4 for $1," how would the number of books change?
5. How much would it cost to buy 50 books at the current sale price?
6. What would be the minimum number of books to get the best deal under this pricing scheme?
7. What is the difference in cost between buying 20 books individually and using the "3 for $1" deal?
8. If you had $15, how many books could you buy using both deals?

**Tip:** Always look for the most efficient deal to maximize the number of items you can buy within a budget.

Discover how to maximize your purchase of old books at a sale using $9.90. Follow a step-by-step solution to determine the greatest number of books you can buy, leveraging different pricing options. Suitable for Grades 4-6 learners.

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