To solve this problem, let's set up the system of equations based on the given nutritional information.

Variables:

• Let $x$ represent the number of cups of rice.
• Let $y$ represent the number of cups of tofu.
• Let $z$ represent the number of cups of peanuts.

Equations based on nutritional goals:

1. Carbohydrates: $48.6x + 6.6y + 34z = 280$
2. Fat: $0x + 11y + 65.5z = 200$
3. Protein: $2x + 26y + 32z = 140$

We can now solve this system of equations using a matrix method. I'll calculate the solution.The solution to the system of equations is:

• Cups of rice: $3.594$
• Cups of tofu: $1.702$
• Cups of peanuts: $2.768$

These amounts of rice, tofu, and peanuts will meet Juan's nutritional goals of 280 grams of carbohydrates, 200 grams of fat, and 140 grams of protein.

Would you like a breakdown of how these numbers satisfy the nutritional requirements?

Here are 5 related questions to consider:

1. How would the nutritional content change if Juan wanted to reduce his fat intake to 150 grams?
2. What would happen if Juan added a fourth food item to his meal, such as vegetables with no fat but extra protein?
3. How would the solution change if we considered different measurement units, such as grams instead of cups?
4. Could Juan achieve the same nutritional goal using different proportions of tofu and peanuts?
5. What happens if the nutritional goals are increased to meet a higher-calorie requirement?

Tip: Solving nutritional problems using matrices helps streamline complex systems of equations with multiple variables.