Question

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

Explanation:

Step1: Define direct variation

For direct variation, we use the formula \( c = kn \), where \( k \) is the constant of variation.

Step2: Find the constant \( k \)

We know \( c = 54 \) when \( n = 9 \). Substitute these values into the formula: \( 54 = k \times 9 \). Solve for \( k \) by dividing both sides by 9: \( k=\frac{54}{9}=6 \).

Step3: Find the cost for \( n = 3 \)

Now that we know \( k = 6 \), use the formula \( c = kn \) with \( n = 3 \). So \( c = 6\times3 = 18 \).

Answer:

\$18 (corresponding to the option: \$18)