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To solve this problem, we need to set up a system of equations based on the information provided about the ingredients and their contributions of protein, carbohydrates, and fat.

Let:
- \( x \) = units of Ingredient A,
- \( y \) = units of Ingredient B,
- \( z \) = units of Ingredient C.

From the problem, we know the following contributions for each ingredient per unit:

|              | Protein (g) | Carbohydrates (g) | Fat (g) |
|--------------|-------------|-------------------|---------|
| Ingredient A |      3      |         3         |    1    |
| Ingredient B |      2      |         4         |    2    |
| Ingredient C |      4      |         5         |    1    |

The target is to create a meal that has:
- 25 grams of protein,
- 35 grams of carbohydrates,
- 13 grams of fat.

We can now write the system of equations based on these totals:

1. For protein: \( 3x + 2y + 4z = 25 \)
2. For carbohydrates: \( 3x + 4y + 5z = 35 \)
3. For fat: \( x + 2y + z = 13 \)

This system can be solved using substitution or elimination. Let's solve it step by step.

### Step 1: Solve for one variable from the third equation
From the fat equation, we have:
\[ x + 2y + z = 13 \]
Solve for \( x \):
\[ x = 13 - 2y - z \]

### Step 2: Substitute into the other two equations
Now, substitute \( x = 13 - 2y - z \) into the protein and carbohydrates equations:

For protein:
\[ 3(13 - 2y - z) + 2y + 4z = 25 \]
\[ 39 - 6y - 

Julia is preparing a meal by combining three ingredients. One unit of each ingredient provides the following quantities (in grams) of carbohydrates, fat, and protein:
- Ingredient A: 3g Protein, 3g Carbohydrates, 1g Fat
- Ingredient B: 2g Protein, 4g Carbohydrates, 2g Fat
- Ingredient C: 4g Protein, 5g Carbohydrates, 1g Fat

The meal should contain 25 grams of protein, 35 grams of carbohydrates, and 13 grams of fat. How many units of each ingredient should Julia use?

Learn how to solve a system of equations to determine the correct number of units of three ingredients (A, B, C) to achieve a meal containing 25 grams of protein, 35 grams of carbohydrates, and 13 grams of fat. The problem involves algebraic methods suitable for Grades 10-12.

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