MATH SOLVE

3 months ago

Q:
# I have tried to to write the inequality for this but not unsure of my answer,please help me. here it is........A college is currently accepting students that are both in-state and out-of-state. They plan to accept two times as many in-state students as out-of-state, and they only have space to accept 200 out-of-state students. Let x = the number of out-of-state students and y = the number in-state students.I think the answer is x>0 and y>0

Accepted Solution

A:

Answers: [tex] 0 \le x \le 200 [/tex][tex] 0 \le y \le 400 [/tex]where x and y are integers==================================================Explanation:x = number of out-of-state studentsy = number of in-state studentsboth x and y are integers (basically numbers that dont have a decimal portion)Given fact 1: "They plan to accept two times as many in-state students as out-of-state"Given fact 2: "they only have space to accept 200 out-of-state students"Because of fact 1 above, we can say y = 2*x or y = 2x. Whatever the x value is, we multiply by 2 to get the y value. Based on fact 2, we know that x cannot exceed 200. Put another way, the largest x can get is 200. So we write [tex] x \le 200 [/tex]. At the same time, x cannot be less than 0, so we also say [tex] x \ge 0 [/tex] which is the same as [tex] 0 \le x [/tex]Combine [tex] 0 \le x [/tex] and [tex] x \le 200 [/tex] to form the compound inequality [tex] 0 \le x \le 200 [/tex]------------From here, multiply all three sides by 2 to get the following[tex] 0 \le x \le 200 [/tex][tex] 2*0 \le 2*x \le 2*200 [/tex][tex] 0 \le 2x \le 400 [/tex][tex] 0 \le y \le 400 [/tex] note the replacement of 2x with y (since y = 2x)which shows that the college will accept up to 400 new in-state students.