Let's denote the number of pounds of walnuts as \( w \) and the number of pounds of almonds as \( a \).
The cost for \( w \) pounds of walnuts, given that walnuts cost $2.00 per pound, can be expressed as:
\[ \text{Cost of } w \text{ pounds of walnuts} = 2w \]
The cost for \( a \) pounds of almonds, given that almonds cost $4.00 per pound, can be expressed as:
\[ \text{Cost of } a \text{ pounds of almonds} = 4a \]
We also know that the total cost of the order is $44, so we can write the equation for total cost:
\[ 2w + 4a = 44 \]
Additionally, we know that the total weight of the nuts is 14 pounds:
\[ w + a = 14 \]
Now we have a system of equations:
- \( 2w + 4a = 44 \)
- \( w + a = 14 \)
You can solve this system of equations to find the values of \( w \) and \( a \). To solve the second equation for \( a \), we get:
\[ a = 14 - w \]
Now we can substitute \( a \) in the first equation:
\[ 2w + 4(14 - w) = 44 \]
Distributing the 4:
\[ 2w + 56 - 4w = 44 \]
Combining like terms:
\[ -2w + 56 = 44 \]
Subtracting 56 from both sides:
\[ -2w = 44 - 56 \]
\[ -2w = -12 \]
Dividing both sides by -2:
\[ w = 6 \]
Now, substituting \( w \) back into the equation for \( a \):
\[ a = 14 - w = 14 - 6 = 8 \]
So, the order consists of:
- Walnuts: 6 pounds
- Almonds: 8 pounds
In summary:
- Number of pounds of walnuts: \( 6 \)
- Number of pounds of almonds: \( 8 \)
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