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

B. 0 < x ≤ 100 and 0 < y ≤ 400 or 300 no different

Explanation:

Answer 2

`0<x\leq 100\ and\ 0<y\leq 300`

Explanation:

Given:

Maximum number of out-of-state students,
`x=100`

Maximum number of in-state students,
`y=3x`

Therefore, the range of out-of-state students can be anywhere between a number greater than 0 but less than or equal to 100 as this is maximum limit.

`0<x\leq 100`

In order to get the interval for
`y`, we multiply the above by 3 throughout.

`3* 0< 3* x\leq 3* 100\\0 < 3x\leq 300`

But
`3x = y`. Therefore,

`0< y\leq 300`