Question

Four consecutive odd integers add up to 64. What are the numbers?

Answer 1

`13, 15, 17 and 19`

Explanation:

Let the first odd number be `=2n+1`, where `n` is any positive integer.

Thus we have four consecutive odd numbers
`(2n+1), (2n+3), (2n+5) and (2n+7)`
Setting the sum of these numbers equal to the given value

`(2n+1)+ (2n+3)+ (2n+5) + (2n+7)=64`, simplifying
`(8n+16)=64`, dividing both sides and solving for `n`
`(n+2)=8`
or `n=8-2=6`
The numbers are
`(2xx6+1), (2xx6+3), (2xx6+5) and (2xx6+7)`
`13, 15, 17 and 19`