In a proportional relationship, the cost (C) is directly proportional to the weight (w) of the deli meat. This can be expressed with the equation:
\[ C = k \cdot w \]
where \( k \) is the constant of proportionality.
To find the constant \( k \), you can use the information provided. Nigel paid $10 for 2.12 pounds of roast beef. Plugging these values into the equation gives:
\[ 10 = k \cdot 2.12 \]
To solve for \( k \):
\[ k = \frac{10}{2.12} \]
Calculating this gives:
\[ k \approx 4.72 \]
Thus, the equation relating the cost \( C \) to the weight \( w \) is:
\[ C = 4.72w \]
This equation describes the proportional relationship between the cost of deli meat and its weight.