Question

school rules permit no fewer than 2 teachers per 25 students. there are at least 245 students enrolled in the school. if x represent teachers and y represents students, which system of linear inequalities can be used to determine the possible number of teachers and students at the school?
○ $2y \geq 25x$ and $y \geq 245$
○ $2y \leq 25x$ and $y \geq 245$
○ $25y \leq 2x$ and $y \geq 245$
○ $25y \geq 2x$ and $y \geq 245$

Explanation:

Step1: Analyze the teacher - student ratio condition

The school rules state that there are no fewer than 2 teachers per 25 students. If \(x\) is the number of teachers and \(y\) is the number of students, the ratio of teachers to students is \(\frac{x}{y}\geq\frac{2}{25}\). Cross - multiplying (since \(y>0\) and \(25 > 0\), the inequality sign remains the same) gives us \(25x\geq2y\), or equivalently \(2y\leq25x\).

Step2: Analyze the number of students condition

It is given that there are at least 245 students enrolled in the school. If \(y\) represents the number of students, then \(y\geq245\).

Answer:

\(2y\leq25x\) and \(y\geq245\) (the second option)