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.

Answer 1

Givens:

• 
  `x` represents the number of out-of-state students.

• 
  `y` represents the number in-state students.

The problem says that the college is planning to accept three times as many in-state students as out-of-state students. This is represented by the equation:

`y=3x`

Also, the problem states that they only have space to accept 100 out-of-state students, this means that
`x` has to be restricted:
`x\leq 100`

These means that the maximum amount of out-of-state students are 100, this also means that the maximum in-state students are 300, because the college is planning to have three times of these students.

At last, the final restrictions would be
`x\geq 0 \ ; \ y\geq  0`, because the number of students cannot be negative, it wouldn't make sense, we cannot say "there are -3 students".

Therefore, all restrictions are:

`x\leq 100`

`x\geq 0 \ ; \ y\geq  0`

`y=3x`

Answer 2

The constraints for the incoming students is written as:

x ≥0, y ≥ 0

x = 3 y

x + y = 100

Explanation:

Let x = the number of out-of-state students

and y = the number in-state students.

Now, number of out state students accepted = 3 times ( In state students)

⇒ x = 3 y

Also, total number of students accepted = 100

So, Number of instate + out state students = 100

⇒ x + y = 100

Now,as x and y are the number of students, so x ≥0, y ≥ 0

Hence, the constraints for the incoming students is written as:

x ≥0, y ≥ 0

x = 3 y

x + y = 100