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Answer :
Let [tex]$x$[/tex] represent the number of teachers and [tex]$y$[/tex] represent the number of students. The school rule states that there must be no fewer than 2 teachers for every 25 students. This statement can be written as a ratio inequality:
[tex]$$
\frac{x}{y} \geq \frac{2}{25}.
$$[/tex]
To eliminate the fraction, multiply both sides of the inequality by [tex]$y$[/tex] (assuming [tex]$y > 0$[/tex], which is valid for a school):
[tex]$$
x \geq \frac{2}{25} y.
$$[/tex]
Next, multiply both sides by 25 to clear the denominator:
[tex]$$
25x \geq 2y.
$$[/tex]
This inequality can be rearranged as:
[tex]$$
2y \leq 25x.
$$[/tex]
In addition to the ratio condition, we are given that there are at least 245 students. This gives the condition:
[tex]$$
y \geq 245.
$$[/tex]
Thus, the possible scenarios for the numbers of teachers and students are described by the inequalities
[tex]$$
2y \leq 25x \quad \text{and} \quad y \geq 245.
$$[/tex]
This matches the second option provided.
[tex]$$
\frac{x}{y} \geq \frac{2}{25}.
$$[/tex]
To eliminate the fraction, multiply both sides of the inequality by [tex]$y$[/tex] (assuming [tex]$y > 0$[/tex], which is valid for a school):
[tex]$$
x \geq \frac{2}{25} y.
$$[/tex]
Next, multiply both sides by 25 to clear the denominator:
[tex]$$
25x \geq 2y.
$$[/tex]
This inequality can be rearranged as:
[tex]$$
2y \leq 25x.
$$[/tex]
In addition to the ratio condition, we are given that there are at least 245 students. This gives the condition:
[tex]$$
y \geq 245.
$$[/tex]
Thus, the possible scenarios for the numbers of teachers and students are described by the inequalities
[tex]$$
2y \leq 25x \quad \text{and} \quad y \geq 245.
$$[/tex]
This matches the second option provided.
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