https://file.aiquickdraw.com/mathbot/file/17254820315724skum92u.jpg

The problem in the image states:

"8. Hector has the same number of $1, $5, and $10 bills. The total value of these bills is $256. How many of each bill does he have?"

Let's solve this problem step by step.

### Let:
- $ x $ be the number of $1 bills.
- $ x $ be the number of $5 bills.
- $ x $ be the number of $10 bills.

### The total value of the bills:
- The value of the $1 bills is $ 1 \times x = x $ dollars.
- The value of the $5 bills is $ 5 \times x = 5x $ dollars.
- The value of the $10 bills is $ 10 \times x = 10x $ dollars.

### Total value equation:
The sum of the values of all the bills equals $256, so:
\[
x + 5x + 10x = 256
\]

### Combine like terms:
\[
16x = 256
\]

### Solve for $ x $:
\[
x = \frac{256}{16} = 16
\]

### Conclusion:
Hector has 16 of each type of bill: 16 $1 bills, 16 $5 bills, and 16 $10 bills.

Would you like further details on any step, or do you have any additional questions?

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Here are 5 related questions to expand your understanding:

1. How would the equation change if Hector had twice as many $5 bills as $1 bills?
2. What if the total value was $512? How would the number of each bill change?
3. How can you set up a similar problem if Hector had 10 more $10 bills than $1 bills?
4. What would the equation look like if the number of $1, $5, and $10 bills were different?
5. How can you verify your solution by checking the total value?

**Tip:** When dealing with problems involving money and identical quantities, setting up an equation that reflects the total value can help simplify the calculation.

Hector has the same number of $1, $5, and $10 bills. The total value of these bills is $256. How many of each bill does he have?

Learn how to solve a linear equation to determine the number of $1, $5, and $10 bills Hector has when the total value is $256. This problem covers algebraic concepts suitable for students in Grades 6-8.

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