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:[tex]0<x\leq 100\ and\ 0<y\leq 300[/tex]Step-by-step explanation:Given:Maximum number of out-of-state students, [tex]x=100[/tex]Maximum number of in-state students, [tex]y=3x[/tex]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.[tex]0<x\leq 100[/tex]In order to get the interval for [tex]y[/tex], we multiply the above by 3 throughout.[tex]3\times 0< 3\times x\leq 3\times 100\\0 < 3x\leq 300[/tex]But [tex]3x = y[/tex]. Therefore,[tex]0< y\leq 300[/tex]