https://file.aiquickdraw.com/mathbot/file/17255037253050z1h6qfn.jpg

Let's analyze the problem step-by-step.

### Given Information:
1. **Mixes and Composition:**
   - Mix A: 5 parts Cashews, 2 parts Macadamias, 3 parts Brazil nuts.
   - Mix B: 4 parts Cashews, 1 part Macadamias, 4 parts Brazil nuts.
   - Mix C: 6 parts Cashews, 1 part Macadamias, 1 part Brazil nuts.
   - The parts are in hundreds of grams.

2. **Costs per Kilogram:**
   - Mix A costs $12.50 per kilogram.
   - Mix B costs $12.40 per kilogram.
   - Mix C costs $11.70 per kilogram.

3. **Goal:**
   - Find the cost per kilogram of each type of nut (Cashews, Macadamias, and Brazil nuts).
   - Calculate the cost to produce a mix containing 400 grams of Cashews, 200 grams of Macadamias, and 400 grams of Brazil nuts.

### Step-by-Step Solution:

1. **Set up equations for cost per kilogram:**

Let:
- $ x $ be the cost per kilogram of Cashews,
- $ y $ be the cost per kilogram of Macadamias,
- $ z $ be the cost per kilogram of Brazil nuts.

Based on the given compositions, we can form the following cost equations:

- **Equation for Mix A:**
  \[
  5x + 2y + 3z = 12.50
  \]

- **Equation for Mix B:**
  \[
  4x + y + 4z = 12.40
  \]

- **Equation for Mix C:**
  \[
  6x + y + z = 11.70
  \]

2. **Solve the system of linear equations:**

Let's solve this system of equations to find the values of $ x $, $ y $, and $ z $.

I will compute these values now.The solution to the system of equations gives us the following costs per kilogram for each type of nut:

- **Cashews (x):** $1.76 per kilogram (rounded to two decimal places)
- **Macadamias (y):** -$0.25 per kilogram (rounded to two decimal places)
- **Brazil nuts (z):** $1.41 per kilogram (rounded to two decimal places)

### Interpretation of the Results:
- The negative cost for Macadamias indicates an issue, likely a mistake in the data provided or the assumptions made in setting up the equations. In real-world terms, negative costs are not feasible, so we should reconsider the information provided or check for errors.

### Next Steps:
1. Review the given cost information for any inconsistencies.
2. Verify if the parts (in hundreds of grams) were interpreted correctly.
3. Reassess if additional constraints or data were not accounted for.

Would you like me to help investigate the cause of the negative cost or proceed with further calculations? Here are a few related questions to consider:

1. Should we check for any possible errors in interpreting the problem's details?
2. Would you like an alternative approach to solve this?
3. Do you want me to verify if there is another possible set of equations?
4. Should we use different units or conversion factors?
5. Do you need further explanations about solving linear systems?

**Tip:** When working with cost equations, always check if the values align with real-world expectations. Negative costs usually indicate a setup or interpretation error.

A mixed nut company uses cashews, macadamias, and Brazil nuts to make three gourmet mixes. If 1kg of Mix A costs $12.50, 1kg of Mix B costs $12.40, and 1kg of Mix C costs $11.70, determine the cost per kilogram of each nut and find the cost to produce a mix containing 400 grams of cashews, 200 grams of macadamias, and 400 grams of Brazil nuts.

This problem involves solving a system of linear equations to determine the cost per kilogram of cashews, macadamias, and Brazil nuts. The solution includes step-by-step calculations based on given costs for different nut mixes. Suitable for high school students studying algebra and linear systems.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation