We will represent our three consecutive odd numbers as [tex] n [/tex], [tex] n + 2 [/tex], and [tex] n + 4 [/tex], where [tex] n [/tex] is an odd integer. (Adding 2 and 4 creates the next odd integers.)
Since the sum of the numbers is 171, we can say their average is [tex] \frac{171}{3} = 57 [/tex]. This means that the average of three three expressions we stated in the beginning is also 57. If we find the average of those three numbers, we get:
[tex] \dfrac{(n) + (n + 2) + (n + 4)}{3} = n + 2 [/tex]
We now know that the average of the three expressions is [tex] n + 2 [/tex]. Since the average is equal to 57, we can find [tex] n [/tex]:
[tex] n + 2 = 57 [/tex]
[tex] n = 55 [/tex]
This means our numbers are 55, 57, and 59. ("Plug" 2 in for [tex] n [/tex] in the expressions we found in the first part of the problem.)
