Join IDNLearn.com and start getting the answers you've been searching for. Whether it's a simple query or a complex problem, our experts have the answers you need.
Sagot :
To determine the system of linear inequalities that represents the school scenario, let's break down the problem step-by-step:
1. Interpreting the Teacher-Student Ratio Requirement:
School rules mandate no fewer than 2 teachers for every 25 students. This requirement implies that the ratio of teachers to students must be at least [tex]\( \frac{2}{25} \)[/tex].
To express this as an inequality:
- Let [tex]\( x \)[/tex] represent the number of teachers.
- Let [tex]\( y \)[/tex] represent the number of students.
- The school rule can be written in terms of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] as [tex]\( \frac{2}{25} \leq \frac{x}{y} \)[/tex].
To eliminate the fraction, we can cross multiply:
[tex]\[ 2y \geq 25x \][/tex]
2. Interpreting the Minimum Number of Students:
There are at least 245 students enrolled in the school.
This can be straightforwardly written as:
[tex]\[ y \geq 245 \][/tex]
Putting these two pieces of information together, we form the system of linear inequalities:
[tex]\[ 2y \geq 25x \quad \text{and} \quad y \geq 245 \][/tex]
This represents the conditions under which the number of teachers and students at the school must operate.
Therefore, the correct system of linear inequalities is:
[tex]\[ 2y \geq 25x \quad \text{and} \quad y \geq 245 \][/tex]
The correct option is:
[tex]\[ 2 y \geq 25 x \quad \text{and} \quad y \geq 245 \][/tex]
1. Interpreting the Teacher-Student Ratio Requirement:
School rules mandate no fewer than 2 teachers for every 25 students. This requirement implies that the ratio of teachers to students must be at least [tex]\( \frac{2}{25} \)[/tex].
To express this as an inequality:
- Let [tex]\( x \)[/tex] represent the number of teachers.
- Let [tex]\( y \)[/tex] represent the number of students.
- The school rule can be written in terms of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] as [tex]\( \frac{2}{25} \leq \frac{x}{y} \)[/tex].
To eliminate the fraction, we can cross multiply:
[tex]\[ 2y \geq 25x \][/tex]
2. Interpreting the Minimum Number of Students:
There are at least 245 students enrolled in the school.
This can be straightforwardly written as:
[tex]\[ y \geq 245 \][/tex]
Putting these two pieces of information together, we form the system of linear inequalities:
[tex]\[ 2y \geq 25x \quad \text{and} \quad y \geq 245 \][/tex]
This represents the conditions under which the number of teachers and students at the school must operate.
Therefore, the correct system of linear inequalities is:
[tex]\[ 2y \geq 25x \quad \text{and} \quad y \geq 245 \][/tex]
The correct option is:
[tex]\[ 2 y \geq 25 x \quad \text{and} \quad y \geq 245 \][/tex]
We appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. IDNLearn.com is dedicated to providing accurate answers. Thank you for visiting, and see you next time for more solutions.