The sum of three consecutive odd numbers is more than 207, how do you find the minimum values of these integers?

1 Answer
Feb 9, 2016

69, 71, and 73

Explanation:

First odd: x
Second odd: x + 2 (2 greater than the first, to skip the even number in between
Third odd: x + 4

Add all three:
x + x + 2 + x + 4 = 3x + 6

Now let's set it to 207:
3x + 6 = 207

Subtract 6:
3x = 201

Divide by 3:
x = 67

So our numbers are
x = 67
x + 2 = 69
x + 4 = 71

....

Not so fast!

67 + 69 + 71 = 207, but we need numbers that are greater than 207!

That's easy, we just need to move the lowest odd (67) to be just more than higheset odd (71). This makes our values:

69, 71, and 73, which sum to 213.