Question

Three consecutive odd integers have a sum of 51. what is the smallest integer

Answer 1

Answer:

15

Step-by-step explanation:

Let 2n+1 be the first odd integer.

Therefore, the consecutive odd integers will be 2n+3 and 2n+5

If the sum of the consecutive odd integers is 51 then:

⇒ 2n + 1 + 2n + 3 + 2n + 5 = 51

⇒ 6n + 9 = 51

⇒ 6n = 42

⇒ n = 7

To find the values of the integers, substitute the found value of n into the expressions:

• First integer:       2(7) + 1 = 15
• Second integer:  2(7) + 3 = 17
• Third integer:      2(7) + 5 = 19

Therefore, the three consecutive odd integers that sum to 51 are 15, 17 and 19.  The smallest of which is 15.