Question

Find 3 consecutive odd numbers whose sum is 219

Answer 1

Sum of 3 consecutive numbers = 219
Average of these numbers = 219/3 = 73
Average of 3 consecutive numbers = ''Middle number'' ...[concept of average]
[Average of 'n' consecutive numbers = middle number,for n=odd..Even if the common difference between the numbers is same,this concept works,provided 'n' is odd]
Hence the second number is 73..Other numbers are 71,75..
So the consecutive odd numbers are 71,73,75

Alternatively:
Let the numbers be x+1 , x+3 , x+5
x+1 + x+3 + x+5 = 219
3x + 9 = 219
3x = 210
x= 210/3 = 70
Hence x+1 = 71...x+3 = 73...x+5 = 75