Question

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.

Answer 1

The constraints to represent the incoming students at the college are $0$ and $0$ 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:

$y = 2x$

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

$0$

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

$0$

Therefore, the correct option is D).

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