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

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Answer 1 · 2016-02-09T21:22:53

#69#, #71#, and #73#

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#.