Let the total number of people be X.

Number of participants in Heping District x/3

The number of participants in Hedong District is 2x/7.

Number of participants in Hebei District x/5

Number of winners in Heping District x/3 * 1/24= x/72.

The number of winners in Hedong District is 2x/7 *116 = x/56.

Number of winners in Hebei district x/5 *118 = x/90.

Because x/72 x/56 x/90 are all integers.

X is divisible by 72 56 90.

And because the least common multiple of 72 56 90 is 2520.

X is a number greater than 2000, and x=2520.