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

Answer:

The constraints for the incoming students is written as:

x ≥0, y ≥ 0

 x =  3 y

 x  + y  = 100

Step-by-step 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

Answer 2

Answer:

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:

$x\leq 100$

$x\geq 0 \ ; \ y\geq  0$

$y=3x$