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

Constraint that represents the incoming students at the college is

y ≤ 300

Explanation:

It is given in this question that a college is currently accepting both in-state and out of state students where,

y = Number of in-state students

x = Number of out-of-state students

Their plan is to accept three times as many in students as out of state

Which is represented by he equation y = 3x

x =
`(y)/(3)`

College has space for 100 out-of-state students only, so the inequality which represents this situation will be

x ≤ 100

Now the constraint to represent the incoming students in the college will be

`(y)/(3)\leq  100`

y ≤ 300

Therefore, constraint that represents the incoming students at the college is y ≤ 300

Answer 2

\[y < = 300\]

Explanation:

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

Let y = number of in-state students at the college

As per the given problem, the constraints are as follows:

\[x < = 100\] --------- (1)

\[y = 3 * x\] --------- (2)

From the given equations (2), \[ x = y/3 \]

Substituting in (1):

\[y/3 < = 100\]

Or, \[y < = 300\] which is the constraint representing the incoming students.