There is a proportional relationship between a volume measured in cups, \(c\), and the same volume measured in tablespoons, \(t\).

3 cups are equivalent to 48 tablespoons.

What is the constant of proportionality for this relationship?

What does this mean in terms of volume measured in cups, \(c\), and the same volume measured in tablespoons, \(t\)?

The constant of proportionality between cups and tablespoons is 16 tablespoons per cup. It indicates that for every cup of volume, there are 16 tablespoons. This constant can be used to convert any cup measurement to tablespoons.

Explanation:

Understanding the Constant of Proportionality

The constant of proportionality is the ratio between two proportional quantities. Given that 3 cups are equivalent to 48 tablespoons, we can determine this constant by dividing the number of tablespoons by the number of cups. The calculation would be 48 tablespoons ÷ 3 cups, which simplifies to 16 tablespoons per cup. This means that for every cup of volume, there are 16 tablespoons. Hence, the constant of proportionality in this relationship is 16.

Example of Using the Constant

If you needed to find out how many tablespoons are in 6 cups, you would simply multiply 6 cups by the constant of proportionality, which is 16 tablespoons per cup. The calculation would be 6 × 16, equaling 96 tablespoons.