Question #cb56b

2 Answers
May 19, 2017

{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}

May 19, 2017

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