At the beginning of each school year, Madison Middle School orders new shirts for the entire student body. Each student receives one shirt. Each shirt is the same price, s, and the school orders enough for n students. Which equation represents the proportional relationship between P, the total price of the shirts, and the number of students?
A.
B.
C.
D.
C. P = sn
explain
The equation P = sn represents the proportional relationship between the total price of the shirts (P) and the number of students (n). This equation states that the total price is equal to the product of the price per shirt (s) and the number of students. This makes sense because if the number of students doubles, then the total price should also double, as each student still receives one shirt.
The equation that represents the proportional relationship between P, the total price of the shirts, and the number of students, can be determined by understanding the definition of a proportional relationship.
In a proportional relationship, two quantities are directly related, which means that as one quantity increases, the other also increases at a consistent ratio.
In this case, the total price of the shirts, P, is directly related to the number of students, n. As the number of students increases, the total price of the shirts will also increase.
To find the proportional relationship equation, we need to express this relationship using variables and coefficients.
Let's analyze the given information:
- Each shirt is the same price, s.
- The school orders enough shirts for n students.
From this information, we can conclude that the total price of the shirts, P, will be the product of the price per shirt, s, and the number of students, n.
Therefore, the equation representing the proportional relationship would be:
P = s * n
Using the information given, we can conclude that the correct equation representing the proportional relationship between P and n is:
D. P = s * n