Let's solve the problem step-by-step.
Given the requirement from the local high school, we have the inequality:
[tex]\[ y \geq \frac{x}{12} \][/tex]
where [tex]\( y \)[/tex] represents the number of adult chaperones and [tex]\( x \)[/tex] represents the number of students.
We need to verify if the ordered pair [tex]\((x, y) = (50, 5)\)[/tex] meets this requirement.
1. Substitute the values into the inequality:
[tex]\[ 5 \geq \frac{50}{12} \][/tex]
2. Simplify [tex]\(\frac{50}{12}\)[/tex]:
[tex]\[ \frac{50}{12} = \frac{25}{6} \approx 4.167 \][/tex]
3. Compare the simplified result with 5:
[tex]\[ 5 \geq 4.167 \][/tex]
This inequality is true because 5 is indeed greater than approximately 4.167.
Thus, the ordered pair [tex]\((50, 5)\)[/tex] satisfies the inequality [tex]\( y \geq \frac{x}{12} \)[/tex].
Given the context of the problem and the fact that the pair [tex]\((50, 5)\)[/tex] meets the requirement, the most appropriate representation of this ordered pair is:
- 5 adult chaperones and 50 students going on the field trip.
Therefore, the correct representation is:
[tex]\[ 5 \text{ adult chaperones and } 50 \text{ students going on the field trip.} \][/tex]
