Question

The mean of six consecutive odd integers is 22 what is the smallest of these numbers

Answer 1

To find the smallest of six consecutive odd integers with a mean of 22, we identify the middle two integers as 21 and 23 and subtract 2 twice from 21, revealing the smallest integer to be 17.

Step-by-step explanation:

The mean of six consecutive odd integers is 22. To find the smallest integer, one approach is to recognize that the mean of any evenly sized set of consecutive numbers is the average of the two middle numbers. Since the mean here is 22, the third and fourth numbers in the set average to 22. Since they are consecutive odd numbers, they must be 21 and 23. Counting backwards, we can find the smallest number by subtracting 2 for each previous consecutive odd number, resulting in the smallest number being 21 - 2 - 2 = 17.

Answer 2

Let the consecutive odd integers be: x-5, x-3, x-1, x+1, x+3, x+5

Mean = 22


`(x-5 +x-3+ x-1+ x+1+ x+3+ x+5)/(6) = 22`


`(6x)/(6) = 22`

x = 22

Hence, the odd integers are 17, 19, 21, 23, 25.

The smallest integer is 17.