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?

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.