Answer:
0 < x ≤ 100 and 0 < y ≤ 300
Explanation:
THIS IS THE COMPLETE QUESTION BELOW;
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
SOLUTION
they only have space to accept 100 out-of-state students,which means that the Maximum number of out-of-state students that can be accepted is 100
Then x= 100(Maximum number of out-of-state students that can be accepted)
They plan to accept three times as many in-state students as out-of-state which means that
Y = 3x(Maximum number of in-state students)
Then we can deduced that the numbee out-of-state students that can be accepted can lyes between the range of 0 and 100 which means from interval 0 to 100
Which can be written as 0 < x ≤ 100
But we need to know the interval for the Maximum number of in-state students(Y), to do that we need to multiply the equation above by 3 since Y = 3x
0 < x ≤ 100
3× 0 = 0
3× X = X
3× 100= 300
Then 0 < 3x≤ 300
But we know that Y = 3x then substitute into last equation
We have
0 < y ≤ 300
ThenBthe constraints to represent the incoming students at the college is
0 < x ≤ 100 and 0 < y ≤ 300