Math Problem Statement
Solve
Solution
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:
- = units of Ingredient A,
- = units of Ingredient B,
- = 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:
- For protein:
- For carbohydrates:
- For fat:
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: Solve for :
Step 2: Substitute into the other two equations
Now, substitute into the protein and carbohydrates equations:
For protein: [ 39 - 6y -
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Math Problem Analysis
Mathematical Concepts
Algebra
System of Equations
Formulas
3x + 2y + 4z = 25
3x + 4y + 5z = 35
x + 2y + z = 13
Theorems
-
Suitable Grade Level
Grades 10-12
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