If Angela had $6w and bought books at $17 each with $w left. How many books did she buy?

Let's solve the problem step by step:

1. **Initial amount of money Angela had**:  
   Angela had $6w.

2. **Amount left after buying books**:  
   After buying the books, Angela had $w left.

3. **Amount spent on books**:  
   The amount spent on books would be the difference between the initial amount and the remaining amount, which is:
   \[
   6w - w = 5w
   \]

4. **Cost of each book**:  
   Each book costs $17.

5. **Number of books bought**:  
   The number of books Angela bought can be found by dividing the total amount spent on books by the cost of one book:
   \[
   \text{Number of books} = \frac{5w}{17}
   \]

So, Angela bought $\frac{5w}{17}$ books. 

To ensure the number of books is an integer, $w$ must be a multiple of 17. If $w$ is such that $\frac{5w}{17}$ is an integer, then that would be the exact number of books she bought.

Would you like to go deeper into any part of this solution or have any questions?

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**Related Questions:**

1. If $ w = 17 $, how many books did Angela buy?
2. What would happen if each book cost $20 instead of $17?
3. How much money would Angela have left if she bought 3 books?
4. What is the minimum value of $ w $ so that Angela can buy at least one book?
5. If Angela had $10w instead of $6w, how many books could she buy?

**Tip:** Always check if your result is a whole number when dealing with quantities like books, which cannot be fractional in most cases.

Learn how to calculate the number of books Angela bought with $6w, given that each book costs $17 and she had $w left after buying. This problem involves basic arithmetic and algebraic reasoning, suitable for students in Grades 5-6.

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