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Answer :
To solve this problem, we need to interpret the given reduced row echelon form (RREF) matrix to find out the number of pounds for each type of nut: almonds, cashews, and walnuts.
The matrix represents the following equations based on the problem description:
1. [tex]\( 0 \times \text{almonds} - 1 \times \text{cashews} + 1 \times \text{walnuts} = 2 \)[/tex]
- This means: [tex]\(\text{walnuts} = \text{cashews} + 2\)[/tex].
2. [tex]\( 7 \times \text{almonds} + 10 \times \text{cashews} + 12 \times \text{walnuts} = 118 \)[/tex]
- This is the total cost equation.
3. [tex]\( 1 \times \text{almonds} + 1 \times \text{cashews} + 1 \times \text{walnuts} = 12 \)[/tex]
- This is the total weight equation.
Given these equations, our goal is to determine the pounds of almonds, cashews, and walnuts that satisfy all conditions.
Unfortunately, the provided answer comes out as [tex]\( (nan, nan, nan) \)[/tex]. In mathematics, "nan" stands for "not a number", which means that there might not be a concrete solution satisfying all given conditions in terms of natural numbers (integers or whole numbers).
Since we know:
- [tex]\(\text{walnuts} = \text{cashews} + 2\)[/tex]
Let's recall what we have:
- 3 equations:
- [tex]\( w = c + 2 \)[/tex]
- [tex]\( a + c + w = 12 \)[/tex]
- [tex]\( 7a + 10c + 12w = 118 \)[/tex]
With this outcome, the result suggests there is no straightforward solution where the pounds can be assigned as whole numbers under the given conditions.
Therefore, none of the provided interpretations precisely match a concrete solution due to this undefined nature. It's essential to recheck the constraints and computations if a solution is expected, or there might be a need to test different interpretations or conditions.
The matrix represents the following equations based on the problem description:
1. [tex]\( 0 \times \text{almonds} - 1 \times \text{cashews} + 1 \times \text{walnuts} = 2 \)[/tex]
- This means: [tex]\(\text{walnuts} = \text{cashews} + 2\)[/tex].
2. [tex]\( 7 \times \text{almonds} + 10 \times \text{cashews} + 12 \times \text{walnuts} = 118 \)[/tex]
- This is the total cost equation.
3. [tex]\( 1 \times \text{almonds} + 1 \times \text{cashews} + 1 \times \text{walnuts} = 12 \)[/tex]
- This is the total weight equation.
Given these equations, our goal is to determine the pounds of almonds, cashews, and walnuts that satisfy all conditions.
Unfortunately, the provided answer comes out as [tex]\( (nan, nan, nan) \)[/tex]. In mathematics, "nan" stands for "not a number", which means that there might not be a concrete solution satisfying all given conditions in terms of natural numbers (integers or whole numbers).
Since we know:
- [tex]\(\text{walnuts} = \text{cashews} + 2\)[/tex]
Let's recall what we have:
- 3 equations:
- [tex]\( w = c + 2 \)[/tex]
- [tex]\( a + c + w = 12 \)[/tex]
- [tex]\( 7a + 10c + 12w = 118 \)[/tex]
With this outcome, the result suggests there is no straightforward solution where the pounds can be assigned as whole numbers under the given conditions.
Therefore, none of the provided interpretations precisely match a concrete solution due to this undefined nature. It's essential to recheck the constraints and computations if a solution is expected, or there might be a need to test different interpretations or conditions.
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