To determine which equation correctly represents the proportional relationship between the number of seats [tex]\( s \)[/tex] and the number of rows [tex]\( r \)[/tex] in an auditorium where there are 100 seats for every 10 rows, let's break down the given information step-by-step:
1. Understanding the Relationship:
- We know there are 100 seats in total for every 10 rows.
2. Finding the Number of Seats per Row:
- If there are 100 seats in 10 rows, we can calculate the number of seats per row by dividing the total number of seats by the total number of rows:
[tex]\[
\text{Seats per row} = \frac{100 \text{ seats}}{10 \text{ rows}} = 10 \text{ seats per row}
\][/tex]
3. Formulating the Equation:
- Since each row has 10 seats, the total number of seats [tex]\( s \)[/tex] can be expressed as 10 times the number of rows [tex]\( r \)[/tex]. Therefore, the equation representing the total number of seats [tex]\( s \)[/tex] in terms of the number of rows [tex]\( r \)[/tex] would be:
[tex]\[
s = 10r
\][/tex]
Given this analysis, the correct equation that represents the proportional relationship is:
A. [tex]\( s = 10r \)[/tex]
