To determine the system of linear inequalities that represents the school scenario, let's break down the problem step-by-step:
1. Interpreting the Teacher-Student Ratio Requirement:
School rules mandate no fewer than 2 teachers for every 25 students. This requirement implies that the ratio of teachers to students must be at least [tex]\( \frac{2}{25} \)[/tex].
To express this as an inequality:
- Let [tex]\( x \)[/tex] represent the number of teachers.
- Let [tex]\( y \)[/tex] represent the number of students.
- The school rule can be written in terms of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] as [tex]\( \frac{2}{25} \leq \frac{x}{y} \)[/tex].
To eliminate the fraction, we can cross multiply:
[tex]\[
2y \geq 25x
\][/tex]
2. Interpreting the Minimum Number of Students:
There are at least 245 students enrolled in the school.
This can be straightforwardly written as:
[tex]\[
y \geq 245
\][/tex]
Putting these two pieces of information together, we form the system of linear inequalities:
[tex]\[
2y \geq 25x \quad \text{and} \quad y \geq 245
\][/tex]
This represents the conditions under which the number of teachers and students at the school must operate.
Therefore, the correct system of linear inequalities is:
[tex]\[
2y \geq 25x \quad \text{and} \quad y \geq 245
\][/tex]
The correct option is:
[tex]\[
2 y \geq 25 x \quad \text{and} \quad y \geq 245
\][/tex]
