A local high school requires at least one adult chaperone for every 12 students, represented by the inequality [tex]y \geq \frac{x}{12}[/tex]. Verify that this rule is met.

What does the ordered pair (50,5) represent?

A. 5 adult chaperones and 50 students going on the field trip
B. 5 students and 50 adult chaperones going on the field trip
C. 50 people going on the field trip, 5 of whom are adult chaperones
D. 50 people going on the field trip, 5 of whom are students



Answer :

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]