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A college is currently accepting students that are both in-state and out-of-state. They plan to accept two times as many in-state students as out-of-state, and they only have space to accept 200 out-of-state students. Let x = the number of out-of-state students and y = the number in-state students. Write the constraints to represent the incoming students at the college. X > 0 and y > 0 0 < x ≤ 200 and y > 400 0 < x and y < 200 0 < x ≤ 200 and 0 < y ≤ 400.

Respuesta :

The constraints to represent the incoming students at the college are [tex]0<x \leq 200[/tex] and [tex]0<y \leq 400[/tex] and this can be determined by using the given data.

Given :

  • College plans to accept two times as many in-state students as out-of-state, and they only have space to accept 200 out-of-state students.
  • x is the number of out-of-state students and y is the number of in-state students.

The following steps can be used in order to determine the constraints to represent the incoming students at the college:

Step 1 - The inequalities are formed in order to determine the constraints to represent the incoming students at the college.

Step 2 - The linear equation that represents the situation "two times as many in-state students as out-of-state" is:

[tex]y = 2x[/tex]

Step 3 - The inequality that represents the situation "college only have space to accept 200 out-of-state students" is:

[tex]0<x \leq 200[/tex]

Step 4 - So, the inequality that represents the maximum number of in-state students that college can take is:

[tex]0<y \leq 400[/tex]

Therefore, the correct option is D).

For more information, refer to the link given below:

https://brainly.com/question/19491153

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