Respuesta :
Answers:
[tex] 0 \le x \le 200 [/tex]
[tex] 0 \le y \le 400 [/tex]
where x and y are integers
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Explanation:
x = number of out-of-state students
y = number of in-state students
both 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]
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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.
