Question

Question #cb56b

Answer 1

`{2n+1, 2n+3, 2n+5}={11, 13, 15}`

Explanation:

If you have three, consecutive odd integers, you could write it like this
`{2n+1, 2n+3, 2n+5}` where `n` is an integer

The `2n` term is guaranteed to be even. So adding an odd value (i.e., 1, 3, and 5) ensures it will be odd.

The smallest odd is `2n+1`. The largest is `2n+5`. The problem tells us that

`2(2n+1)=2n+5+7`
`4n+2=2n+12`
`2n+2=12` (subtract `2n` from both sides)
`2n=10` (subtract `2` from both sides)
`n=5`

Plugging `n=5` back into our three consecutive integers gives
`{2n+1, 2n+3, 2n+5}={11, 13, 15}`

Answer 2

Let `x` be the smallest of the three consecutive odd integers. Then the three consecutive odd integers are:
`x, x+2, x+4`

`2x = 7+(x+4)`
Left side of the equation comes from "Twice the smallest"
Right side of the equation comes from "seven more than the largest"

`2x=x+11`

x=11

Since we have `x` now, the three consecutive odd integers are:
`11, 11+2, 11+4`

`11, 13, 15`