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Answer :
Let's go through the problem step-by-step to interpret the situation described by the given matrix.
The customer buys three types of nuts: almonds (let's call the amount [tex]\(x\)[/tex]), cashews ([tex]\(y\)[/tex]), and walnuts ([tex]\(z\)[/tex]).
We have the following information from the problem statement and the matrix:
1. Equation for walnuts and cashews:
[tex]\[
z = y + 2
\][/tex]
This equation comes from the first row of the matrix [tex]\([0, -1, 1, 2]\)[/tex], which represents [tex]\(0x - y + z = 2\)[/tex].
2. Cost equation:
[tex]\[
7x + 10y + 12z = 118
\][/tex]
This comes from the second row of the matrix [tex]\([7, 10, 12, 118]\)[/tex].
3. Total weight equation:
[tex]\[
x + y + z = 12
\][/tex]
This comes from the third row of the matrix [tex]\([1, 1, 1, 12]\)[/tex].
To find the correct interpretation, let's test each statement:
1. Statement: "The customer buys 1 more pound of walnuts than almonds and 1 more pound of almonds than cashews."
This suggests:
- [tex]\(z = x + 1\)[/tex]
- [tex]\(x = y + 1\)[/tex]
Combining these:
- [tex]\(z = y + 2\)[/tex] which is consistent with the matrix.
2. Statement: "The customer buys 2 more pounds of walnuts than almonds and 2 more pounds of almonds than cashews."
This suggests:
- [tex]\(z = x + 2\)[/tex]
- [tex]\(x = y + 2\)[/tex]
Combining these:
- [tex]\(z = y + 4\)[/tex] which is not consistent with the matrix.
3. Statement: "The customer buys 0.5 more pounds of walnuts than almonds and 2.5 more pounds of almonds than cashews."
This suggests:
- [tex]\(z = x + 0.5\)[/tex]
- [tex]\(x = y + 2.5\)[/tex]
Combining these:
- [tex]\(z = y + 3\)[/tex] which is not consistent with the matrix.
4. Statement: "The customer buys 6.5 more pounds of walnuts than almonds and 8.5 more pounds of almonds than cashews."
This suggests:
- [tex]\(z = x + 6.5\)[/tex]
- [tex]\(x = y + 8.5\)[/tex]
Combining these:
- [tex]\(z = y + 15\)[/tex] which is not consistent with the matrix.
The first statement fits the condition [tex]\(z = y + 2\)[/tex] described by the matrix. Therefore, the correct interpretation of the results is:
"The customer buys 1 more pound of walnuts than almonds and 1 more pound of almonds than cashews."
The customer buys three types of nuts: almonds (let's call the amount [tex]\(x\)[/tex]), cashews ([tex]\(y\)[/tex]), and walnuts ([tex]\(z\)[/tex]).
We have the following information from the problem statement and the matrix:
1. Equation for walnuts and cashews:
[tex]\[
z = y + 2
\][/tex]
This equation comes from the first row of the matrix [tex]\([0, -1, 1, 2]\)[/tex], which represents [tex]\(0x - y + z = 2\)[/tex].
2. Cost equation:
[tex]\[
7x + 10y + 12z = 118
\][/tex]
This comes from the second row of the matrix [tex]\([7, 10, 12, 118]\)[/tex].
3. Total weight equation:
[tex]\[
x + y + z = 12
\][/tex]
This comes from the third row of the matrix [tex]\([1, 1, 1, 12]\)[/tex].
To find the correct interpretation, let's test each statement:
1. Statement: "The customer buys 1 more pound of walnuts than almonds and 1 more pound of almonds than cashews."
This suggests:
- [tex]\(z = x + 1\)[/tex]
- [tex]\(x = y + 1\)[/tex]
Combining these:
- [tex]\(z = y + 2\)[/tex] which is consistent with the matrix.
2. Statement: "The customer buys 2 more pounds of walnuts than almonds and 2 more pounds of almonds than cashews."
This suggests:
- [tex]\(z = x + 2\)[/tex]
- [tex]\(x = y + 2\)[/tex]
Combining these:
- [tex]\(z = y + 4\)[/tex] which is not consistent with the matrix.
3. Statement: "The customer buys 0.5 more pounds of walnuts than almonds and 2.5 more pounds of almonds than cashews."
This suggests:
- [tex]\(z = x + 0.5\)[/tex]
- [tex]\(x = y + 2.5\)[/tex]
Combining these:
- [tex]\(z = y + 3\)[/tex] which is not consistent with the matrix.
4. Statement: "The customer buys 6.5 more pounds of walnuts than almonds and 8.5 more pounds of almonds than cashews."
This suggests:
- [tex]\(z = x + 6.5\)[/tex]
- [tex]\(x = y + 8.5\)[/tex]
Combining these:
- [tex]\(z = y + 15\)[/tex] which is not consistent with the matrix.
The first statement fits the condition [tex]\(z = y + 2\)[/tex] described by the matrix. Therefore, the correct interpretation of the results is:
"The customer buys 1 more pound of walnuts than almonds and 1 more pound of almonds than cashews."
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