Answer:
13, 15, 17 are the three consecutive odd numbers.
Explanation:
Consecutive odd numbers are separated from the preceding and succeeding ones by a value of 2
For example, 1, 3 and 5 are three consecutive numbers and the difference between successive numbers is 2
If m - 1 is the middle integer
then the first integer = (m-1) - 2 = m-3
The third integer = (m - 1) + 2 = m + 1
It is given that the sum of the three consecutive odd integers is 45
So (m - 3) + (m - 1) + (m + 1) = 45
Expanding the brackets
m - 3 + m - 1 + m + 1 = 45
Grouping like terms
m + m + m -3 -1 + 1 = 45
3m - 3 = 45
3m = 45 + 3 = 48
m = 48/3 = 16
So the three integers are
m - 3 = 16 - 3 = 13
m -1 = 16 - 1 = 15
m + 1 = 16 + 1 = 17
13, 15 and 17 are the three consecutive odd integers
Sidenote
An alternate approach is to realize that the middle number in a set of 3 consecutive numbers is the average = total/3 = 45/3 = 15
So the middle number is 15, the first number is 15 - 2 = 13 and the last number is 15+2 = 17
Choose whichever method of solution is easier for you to understand