Question

functons will be opening a new high school in the fall. the number of underclassmen (9th and 10th graders) must fall between 450 and 600 (inclusive). the number of upperclassmen (11th and 12th graders) must be greater than 550 but less than 700. the total number of students cannot exceed 1300. the number of underclassmen needs to exceed the number of upperclassmen. let x represent the number of underclassmen and let y represent the number of upperclassmen. write a system of inequalities that models the constraints on the composition of the student body. then there are three systems of inequalities as options: 1. \\(\

$$\begin{cases} 450 < x < 600 \\\\ 550 < y < 700 \\\\ y > x \\end{cases}$$

\\) 2. \\(\

$$\begin{cases} 450 \\leq x \\leq 600 \\\\ 550 < y < 700 \\\\ x + y \\leq 1300 \\\\ x > y \\end{cases}$$

\\) 3. \\(\

$$\begin{cases} 450 < x < 600 \\\\ 550 < y < 700 \\\\ x + y > 1300 \\\\ x > y \\end{cases}$$

\\)

Explanation:

Step1: Define underclassmen constraint

Underclassmen ($x$) between 450 and 600 inclusive: $450 \leq x \leq 600$

Step2: Define upperclassmen constraint

Upperclassmen ($y$) >550 and <700: $550 < y < 700$

Step3: Total students constraint

Total ≤1300: $x + y \leq 1300$

Step4: Underclassmen exceed upperclassmen

$x > y$

Answer:

B.

$$\begin{cases} 450 \leq x \leq 600 \\ 550 < y < 700 \\ x + y \leq 1300 \\ x > y \end{cases}$$