To evaluate the expression \(7 (1 + 2w)\), we first need to identify the variables in the expression:
- \(w\) is the width of the garden.
- \(l\) is the length of the garden, but it's not part of the expression directly.
Given that:
- Length \(l = 5\) yards
- Width \(w = 2\) yards
Now substituting \(w = 2\) into the expression:
\[ 7(1 + 2w) = 7(1 + 2 \cdot 2) \] \[ = 7(1 + 4) \] \[ = 7 \cdot 5 \] \[ = 35 \]
However, since this does not match any of the options provided, let's understand what the expression might be implying regarding the total perimeter of the fence.
The expression \(1 + 2w\) could be interpreted as including the length \(l\):
Thus the total perimeter \(P\) of the garden is: \[ P = 2l + 2w \]
Substituting the values:
\[ P = 2(5) + 2(2) \] \[ = 10 + 4 \] \[ = 14 \text{ yards} \]
Now we can calculate the cost:
The cost of the fencing is \(7\) dollars per yard: \[ \text{Cost} = 7 \cdot 14 = 98 \]
Therefore, the correct answer is:
$98