Question

A college is currently accepting students that are both in-state and out-of-state. They plan to accept three times as many in-state students as out-of-state, and they only have space to accept 100 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.

0 < x ≤ 100 and 0 < y ≤ 300
x > 0 and y > 0
0 < x ≤ 100 and y > 300
0 < x and y < 100

Answer 1

The college's constraints for accepting students are 0 < x ≤ 100 for out-of-state students and 0 < y ≤ 300 for in-state students, with the in-state students being three times the number of out-of-state students. The correct answer is option 1.

Step-by-step explanation:

The constraints for the number of students that a college is accepting are based on the conditions provided: the college plans to accept three times as many in-state students as out-of-state students, and they only have space to accept 100 out-of-state students.

With x defined as the number of out-of-state students and y as the number of in-state students, we can establish the constraints for x and y. Given that the college can only accept up to 100 out-of-state students, which means 0 < x ≤ 100. Since they accept three times as many in-state students as out-of-state, we can also determine that 0 < y ≤ 300 because the maximum number of in-state students (y) would be 300 if there are 100 out-of-state students (x).

Therefore, the correct constraints representing the incoming students at the college would be: 0 < x ≤ 100 and 0 < y ≤ 300. Hence, the correct option is 0 < x ≤ 100 and 0 < y ≤ 300.