Find all sets of three consecutive odd integers whose sum is between 20 and 30

3 odd numbers sum between 20 & 30

 you get n +n+2+n+4 = between 20 & 30

3n+6 = between 20 & 30

subtract 6 from all 3 numbers you now have 3n = between 14 and 24

 divide all 3 by 3 to get n = between 14/3 and 8

14/3 = 4 2/3

 the only odd numbers between 4 2/3 and 8 are 5 & 7

 so you have 5 + (5+2) + (5+4) = 21

and 7 + (7+2) + (7+4) = 27