To solve this problem, let's go through a step-by-step process:
1. Understand the Relation: The cost [tex]\( c \)[/tex] varies directly with the number of sandwiches [tex]\( n \)[/tex]. This means there is a constant [tex]\( k \)[/tex] such that [tex]\( c = k \cdot n \)[/tex].
2. Find the Constant [tex]\( k \)[/tex]: Given that the cost is \[tex]$54 when the number of sandwiches \( n \) is 9, we can substitute these values into the equation to find \( k \).
\[
54 = k \cdot 9
\]
Solving for \( k \), we get:
\[
k = \frac{54}{9} = 6
\]
Therefore, each sandwich costs \$[/tex]6.
3. Determine the Cost for 3 Sandwiches: Now that we know the cost per sandwich (\[tex]$6), we can find the cost for 3 sandwiches by multiplying the cost per sandwich by the number of sandwiches.
\[
\text{Cost for 3 sandwiches} = 6 \cdot 3 = 18
\]
The cost when \( n \) is 3 is therefore \$[/tex]18.
By evaluating the choices, we can confirm that the correct answer is:
[tex]\[
\$ 18
\][/tex]
