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A number of students are evenly spaced around a circle. the fourth student is directly opposite to the tenth student. how may students are in the circle

User Belgi
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2 Answers

4 votes

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.

User Moritz
by
7.8k points
6 votes

Answer:

12

Step-by-step explanation:

Look at a clock. 4 is opposite 10 on a clock with 12 numbers.

User Petra
by
7.8k points

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