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This problem involves creating a system of equations to determine how many tubes of food A and food B are required to meet nutritional requirements.

### Given information:
1. **Food A**:
   - 4 units of protein
   - 2 units of carbohydrates
   - 2 units of fat
   - Weight: 2 pounds

2. **Food B**:
   - 3 units of protein
   - 6 units of carbohydrates
   - 1 unit of fat
   - Weight: 3 pounds

### Nutritional Requirements:
- 48 units of protein
- 42 units of carbohydrates
- 20 units of fat

We need to find the number of tubes of food A (denoted as \( x \)) and food B (denoted as \( y \)) that meet these nutritional requirements.

### Formulating the system of equations:
From the given information, we can set up the following three equations based on protein, carbohydrates, and fat content:

1. **Protein**: \( 4x + 3y = 48 \)
2. **Carbohydrates**: \( 2x + 6y = 42 \)
3. **Fat**: \( 2x + 1y = 20 \)

Now, I'll solve this system of equations.It seems that the system of equations has no solution in its current form. This could indicate an inconsistency in the provided nutritional information or a mistake in the formulation of the problem.

Let's double-check the formulation of the system and the values. Would you like me to review the problem conditions again or assist with another approach to solving it?

A nutritionist, working for NASA, must meet certain minimum nutritional requirements and yet keep the weight of the food at a minimum. He is considering a combination of two foods, which are packaged in tubes. Each tube of food A contains 4 units of protein, 2 units of carbohydrates, and 2 units of fat and weighs 2 pounds. Each tube of food B contains 3 units of protein, 6 units of carbohydrates, and 1 unit of fat and weighs 3 pounds. The requirement calls for 48 units of protein, 42 units of carbohydrates, and 20 units of fat. How many tubes of each food should be supplied to the astronauts?

This problem involves solving a system of linear equations to determine how many tubes of food A and food B a NASA nutritionist should provide to meet the astronauts' nutritional requirements. Key topics include linear algebra and systems of equations, suitable for high school students in Grades 9-12.

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