The cost, \( c \), of a ham sandwich at a deli varies directly with the number of sandwiches, \( n \). If \( c=\$ 54 \) when \( n \) is 9 , what is the cost of the sandwiches when \( n \) is 3 ? \( \$ 18 \) \( \$ 21 \) \( \$ 27 \) \( \$ 48 \)

To solve this problem, we first need to determine the constant of variation. Since the cost \( c \) varies directly with the number of sandwiches \( n \), we can express this relationship mathematically as \( c = k \cdot n \), where \( k \) is the constant of variation. Given \( c = 54 \) when \( n = 9 \), we can find \( k \) by rearranging the equation: \[ k = \frac{c}{n} = \frac{54}{9} = 6. \] Now that we have \( k \), we can find the cost of the sandwiches when \( n = 3 \): \[ c = k \cdot n = 6 \cdot 3 = 18. \] Thus, the cost of the sandwiches when \( n \) is 3 is \( \$ 18 \). For a bit of fun trivia – did you know that the concept of direct variation isn't just confined to sandwiches? It's a principle that can be applied in various fields, such as physics, economics, and even cooking! For instance, if you're making a batch of cookies, the amount of flour typically varies directly with the number of cookies you are baking. Next time you're at a deli, think about this: understanding ratios and direct relationships can help you make better decisions about food budgeting. It’s not just about the sandwiches! Whether you're cooking or shopping, mastering this concept can help you save money and optimize your meals – so, keep those ratios in mind!