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.