Sample Problem

There is 200-meter long circular track in a school. If workers bury pegs in the ground every 2 meters, there are pegs needed.


 In this lesson, we will be planting trees or placing flags on closed loops. This will be different from planting trees in lines because there will be one extra interval between trees. Before, the first tree in the line and the last tree in the line were only part of 1 interval, now they are part of 2.

To solve this problem, choose one of the pegs and say that it is the first one, or 0 meters away from the first one. The second peg will be 2 meters away from the first one, the third will be 4 meters away and so on. If a peg was 200 meters away from the first one, it would be on top of it because the track is 200 meters long, so the last peg can only be 198 meters away. There is then one peg for every multiple of 2 between 0 and 198. This is equal to the number of multiples of 2 between 2 and 200, so there are 200 ÷ 2 = 100 pegs needed.