Posted by **Roy** on Monday, September 14, 2009 at 8:57pm.

find three consecutive even intergers for which the sum of the first two integers is greater than 9 more than the third integer, and the sum of the first and third integers is less than 17 more than the second integer

- Math -
**MathMate**, Monday, September 14, 2009 at 9:19pm
"find three consecutive even intergers"

Let M be the middle integer.

The three numbers are M-2, M, M+2

"the sum of the first two integers is greater than 9 more than the third integer"

(M-2 + M) > M+2 + 9

on solving

M > 13

"sum of the first and third integers is less than 17 more than the second integer"

M-2 + M+2 < M+17

on solving

M < 17

That leaves us with two choices,

M=14, or M=16.

Check:

M=14

12+14=26 > 16+9=25 OK

12+16=28 < 14+17=31 OK

M=16

14+16=30 > 18+9=27 OK

14+18=32 < 16+17=33 OK

So there are two valid solutions,

12,14,16 or 14,16,18

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