The cost per person of eating in a buffet is c, and the number of persons eating is n. If k is the constant of proportionality, find the equation of variation?
A. c = kn
B. k = n / c
C. c = k / n
D. n = c / k
Answer (2)
To solve this problem, we need to understand the concept of variation. The question implies that the cost per person c is related to the number of persons n by a constant of proportionality k . This is a classic example of direct variation.
In direct variation, one quantity is directly proportional to another. The formula that represents direct variation is:
c = kn
Here, c is the cost per person, n is the number of people, and k is the constant of proportionality. This equation states that the cost per person will increase linearly as the number of people increases, with the constant k determining the rate of that increase.
Breaking it down:
Cost per Person c : This is the amount each individual needs to pay in the buffet.
Number of People n : This is the total number of people dining at the buffet.
Constant of Proportionality k : This constant helps relate the total cost to the number of people, showing that the overall cost increases linearly with the number of individuals.
Therefore, the correct equation of variation from the given options is c = kn , which corresponds to option A.
The equation of variation relating the cost per person and the number of persons is c = kn . This means that the cost per person increases directly with the number of individuals eating, with k as the constant. The correct choice is option A.
;
