To find the equation that represents the proportional relationship between [tex]\(P\)[/tex], the total price of the shirts, and the number of students [tex]\(n\)[/tex], we need to consider how the total price is determined.
Each student receives one shirt, and each shirt costs [tex]\(s\)[/tex] dollars. Therefore, the total cost for the shirts for all the students can be found by multiplying the number of students [tex]\(n\)[/tex] by the price per shirt [tex]\(s\)[/tex].
Thus, the total price [tex]\(P\)[/tex] can be calculated using the following equation:
[tex]\[ P = s \times n \][/tex]
Now, let's review the provided options to identify which one matches this relationship:
A. [tex]\(\div \frac{1}{n}=P\)[/tex] – This option does not make sense in terms of forming an equation involving total price.
B. [tex]\( s n = P \)[/tex] – This exactly matches our derived equation.
C. [tex]\( s + n = P \)[/tex] – This implies adding the price of one shirt and the number of students, which doesn't correctly represent the cost.
D. [tex]\(\frac{n}{3}=P\)[/tex] – This implies dividing the number of students by 3, which doesn't align with calculating the total price.
The correct answer is:
[tex]\[ B. \, s n = P \][/tex]
