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Answer :
To address this problem, we're trying to find the correct inequalities that represent the relationship between the number of teachers and students at a school.
1. Understanding the rules:
- The school requires at least 2 teachers for every 25 students. This can be represented as an inequality:
[tex]\[
2x \geq 25y
\][/tex]
Where [tex]\( x \)[/tex] is the number of teachers and [tex]\( y \)[/tex] is the number of students.
2. Minimum number of students:
- There are at least 245 students enrolled in the school, which means:
[tex]\[
y \geq 245
\][/tex]
3. Finding the correct inequality:
- We're looking for a condition that involves these two points.
- To better match the form we're looking for in the options provided, we can rearrange the inequality [tex]\( 2x \geq 25y \)[/tex] to:
[tex]\[
25y \leq 2x
\][/tex]
- That's equivalent to ensuring that the number of teachers [tex]\( x \)[/tex] is at least sufficient for the number of students [tex]\( y \)[/tex], following the school rule.
Therefore, the statement that aligns with our given conditions is:
[tex]\[
25y \geq 2x \quad \text{and} \quad y \geq 245
\][/tex]
This means the correct choice among the given options would be:
[tex]\[
25y \geq 2x \quad \text{and} \quad y \geq 245
\][/tex]
This reflects the requirement to always have enough teachers for the students, respecting both the proportion rule and the minimum number of students.
1. Understanding the rules:
- The school requires at least 2 teachers for every 25 students. This can be represented as an inequality:
[tex]\[
2x \geq 25y
\][/tex]
Where [tex]\( x \)[/tex] is the number of teachers and [tex]\( y \)[/tex] is the number of students.
2. Minimum number of students:
- There are at least 245 students enrolled in the school, which means:
[tex]\[
y \geq 245
\][/tex]
3. Finding the correct inequality:
- We're looking for a condition that involves these two points.
- To better match the form we're looking for in the options provided, we can rearrange the inequality [tex]\( 2x \geq 25y \)[/tex] to:
[tex]\[
25y \leq 2x
\][/tex]
- That's equivalent to ensuring that the number of teachers [tex]\( x \)[/tex] is at least sufficient for the number of students [tex]\( y \)[/tex], following the school rule.
Therefore, the statement that aligns with our given conditions is:
[tex]\[
25y \geq 2x \quad \text{and} \quad y \geq 245
\][/tex]
This means the correct choice among the given options would be:
[tex]\[
25y \geq 2x \quad \text{and} \quad y \geq 245
\][/tex]
This reflects the requirement to always have enough teachers for the students, respecting both the proportion rule and the minimum number of students.
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