The sum of three consecutive odd numbers is 33. What are the numbers?

Question

Philoid · Accepted Answer

Let the three consecutive odd numbers be 2x + 1,2x + 3,2x + 5(we take 2x + 1 to make sure that it is not divisible by 2,i.e. it is a odd number(here x is a natural number))

Their sum = 33

⇒ 2x + 1 + 2x + 3 + 2x + 5 = 33

⇒ 6x + 9 = 33

⇒ 6x = 33-9

⇒ 6x = 24

⇒

⇒ x = 4

⇒ 2x + 1 = 2 × 4 + 1 = 9

2x + 3 = 2 × 4 + 3 = 11

2x + 5 = 2 × 4 + 5 = 13

Hence, the required three consecutive odd numbers are 9,11 and 13.