1oz of walnuts were mixed with 4oz of peanuts which cost $4/oz to make mixed nuts which cost $5/oz.  What is the price per oz of walnuts?

Let's solve the problem step by step.

### Step 1: Define Variables
- Let $ x $ be the price per ounce of walnuts.

### Step 2: Set Up the Equation
The total cost of the mixed nuts is a weighted average of the costs of walnuts and peanuts. The equation to represent this is:

\[
\text{Total cost} = \text{Cost of walnuts} + \text{Cost of peanuts}
\]

The cost of the mixed nuts can also be expressed as:

\[
\text{Total cost} = (\text{Total weight}) \times (\text{Price per ounce of mixed nuts})
\]

Now let's set up the equation:

\[
1 \times x + 4 \times 4 = (1 + 4) \times 5
\]

### Step 3: Simplify the Equation
Now, simplify the equation:

\[
x + 16 = 5 \times 5
\]

\[
x + 16 = 25
\]

### Step 4: Solve for $ x $
Subtract 16 from both sides:

\[
x = 25 - 16
\]

\[
x = 9
\]

### Conclusion
The price per ounce of walnuts is **$9**.

Would you like more details or have any questions? Here are some related problems to explore:

1. If the price of peanuts was $3/oz instead of $4/oz, what would be the new price per ounce of walnuts?
2. How would the problem change if the mixed nuts were sold for $6/oz instead of $5/oz?
3. What if you mixed 2 oz of walnuts with 4 oz of peanuts? What would the price per ounce of walnuts be in that case?
4. How much would it cost to make 10 oz of these mixed nuts?
5. If you were to mix in a third type of nut at $7/oz, how would you calculate the new mixture cost?

**Tip:** When solving mixture problems, setting up equations based on the total cost and the average price per unit often simplifies finding the unknown variable.

1oz of walnuts were mixed with 4oz of peanuts which cost $4/oz to make mixed nuts which cost $5/oz. What is the price per oz of walnuts?

Learn how to calculate the price per ounce of walnuts when mixed with peanuts to form a $5/oz nut mix. This problem involves algebraic concepts such as weighted averages and linear equations, suitable for students in Grades 8-10.

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