Let's set up the problem using the given information and create a table to organize the data.

Table

	Ingredient 1	Ingredient 2	Mixture
Type	Peanuts	Chocolate	Trail Mix
Price/lb	$2.65	$5.15	$3.47
Weight	$x$	$17 - x$	17 lbs

Now, we'll create a single equation using $x$ to represent the pounds of peanuts.

Mixture Cost Calculation

1. Cost of peanuts: $2.65x$
2. Cost of chocolate: $5.15(17 - x)$
3. Total cost of the mixture: $3.47 \times 17$

Since the total cost of the mixture is the sum of the costs of peanuts and chocolate, we can set up the equation:

$2.65x + 5.15(17 - x) = 3.47 \times 17$

Let's solve the equation:

$2.65x + 5.15(17 - x) = 3.47 \times 17$

$2.65x + 5.15(17 - x) = 58.99$

$2.65x + 87.55 - 5.15x = 58.99$

$-2.5x + 87.55 = 58.99$

$-2.5x = 58.99 - 87.55$

$-2.5x = -28.56$

$x = \frac{-28.56}{-2.5}$

$x = 11.4$

Thus, the pounds of peanuts, $x$, is $11.4$. The pounds of chocolate, $17 - x$, is:

$17 - 11.4 = 5.6$

Pounds of peanuts = 11.4

Pounds of chocolate = 5.6

Would you like further details or have any questions? Here are some related questions to consider:

1. What would be the total cost if we increased the amount of chocolate by 2 lbs?
2. How would the cost per pound of the mixture change if the price of peanuts increased?
3. How would you solve the problem using the Two Variables method?
4. Can we use a different type of candy with a different price per pound and still achieve the same cost per pound for the mixture?
5. How would the solution change if we only had 15 lbs of the mixture?
6. What is the significance of the variable $x$ in this context?
7. How would the problem change if the mixture had to be worth $4.00 per pound instead of $3.47?
8. What other scenarios can we use this one-variable method for?

Tip: When working on mixture problems, always make sure to balance the cost per pound by taking into account both the quantity and the price of each component.