Final answer:
The cost of alcohol varies directly with the volume indicating a constant proportionality rate between the two, represented mathematically by the equation c = kv, where k is the constant of proportionality, and c and v are the cost and volume, respectively.
Step-by-step explanation:
The question involves expressing a relationship between two quantities as a mathematical equation. The cost (c) of alcohol varies directly as its volume (v) in milliliters. This direct variation means that if the volume increases, the cost also increases at a constant rate. The equation representing this relationship can be written as c = kv, where k is the constant of proportionality. In practical terms, for example, if a 5% v/v alcohol solution indicates that there are 5 mL of alcohol per 100 mL of solution, and this ratio is consistent, the cost would vary in direct proportion to the volume of alcohol purchased.
When working with direct and indirect proportionalities, it's essential to understand the behavior of the relationship between the variables. In this case, since the cost varies directly with the volume, we assume a linear relationship, which is described by the equation provided. If we know the cost for a particular volume, we can determine the constant k and use it to find the cost for any other volume. It's important to note that both volumes should be expressed in the same units for this equation to be valid.