Answer: 12
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Step-by-step explanation:
Here's one approach. There are possibly multiple ways to solve this problem.
Consider a circular running track that is 1 mile in circumference. In other words, this is the perimeter of the circle.
Now let's say we had n people. We don't know what number replaces this variable just yet. The only things we know is that it's a positive whole number and that it's 10 or larger.
If the students are evenly spaced around the track, then the space between each adjacent student is 1/n of a mile. For example, if we had 4 students, then the space between each adjacent student is 1/n = 1/4 of a mile.
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Now consider there's a very long rope that wraps around the circular track. This rope can be straightened out to form a number line. Imagine the rope is marked as a ruler.
The space between student 1 and student 2 is 1/n of a mile.
The gap from student 1 to student 4 is 4*(1/n) = 4/n of a mile. Let's call this quantity A.
Then the gap from student 1 to student 10 is 10*(1/n) = 10/n of a mile. Let's call this B.
The difference of A and B tells us the gap from students 4 to 10, so it would be B - A = 10/n - 4/n = (10-4)/n = 6/n
This gap must be exactly 1/2 the circle, aka 1/2 a mile, if we wanted student number 4 to be diametrically opposite student number 10.
Therefore,
6/n = 1/2
6*2 = n*1
12 = n
n = 12
There are 12 students in this circle.
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As I'm wrapping this up, I'm realizing that the solution is as trivial as looking at a round analog clock.
However, I'll keep the steps shown above because your teacher may have a similar problem involving other students being opposite one another. For instance, what if s/he asked "how many students are there if student number 3 is opposite student number 12?"
There's probably also a much more efficient way to do this, so feel free to follow that path if it's much easier that way.