SOLUTION: Find three consecutive odd integers whose sum is three times the third integer

Question 126673: Find three consecutive odd integers whose sum is three times the third integer
Found 2 solutions by bucky, solver91311:
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Consecutive odd integers are 2 digits apart (think of 3 and 5 and 7 as being consecutive
odd integers). So if we let x represent the first odd integer, the next consecutive odd
integer is x + 2 and the next consecutive odd integer after x + 2 is x + 4.
.
Then three times the third integer is 3*(x + 4) which multiplies out to 3x + 12.
.
The problem tells you that the sum of the three consecutive odd integers is 3 times the
third integer. In equation form this can be written as:
.
x + (x + 2) + (x + 4) = 3x + 12
.
On the left side of this equation combine the like terms to get:
.
3x + 6 = 3x + 12
.
What happens if you subtract 3x from both sides? This reduces the "equation" to
.
6 = 12
.
And that obviously cannot be and is not true. This tells you that there is no value of
x that will satisfy this problem. That further means that there are no 3 consecutive
odd integers that add together to give you a sum equal to 3 times the third of the three
consecutive odd integers.
.
Hope this helps you to understand why you were having a problem with this exercise.
.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
If the first odd integer is x, the second one would be x + 2, and the third one would be x + 4.

The sum of the three is but this is equal to 3 times the third odd integer

Adding -3x to both sides of the equation leads to the absurdity that . Therefore, there is no solution to the problem as stated.

Had the problem said 3 times the SECOND integer we would have achieved the result that -- true no matter what x is. Meaning that any three consecutive odd integers would exhibit the property that their sum is equal to 3 times the second integer. In fact, any three consecutive EVEN integers, or just any three consecutive integers also exhibit the same property.
RELATED QUESTIONS
Find three consecutive odd integers whose sum is 10 less than 4 times the least... (answered by stanbon)
Find three consecutive odd integers whose sum is 10 less than 4 times the least... (answered by College Student)
Find all sets of three consecutive odd integers whose sum is at least 47 less than 4... (answered by robertb,mananth)
Find three consecutive odd integers such that the third integer is 3 times the first... (answered by josgarithmetic)
Five times the second of three consecutive odd integers is thirteen less than three times (answered by josmiceli)
Five times the second of three consecutive odd integers is twelve less than three times... (answered by CubeyThePenguin)
Find three consecutive odd integers such that the sum of the second and third integers is (answered by College Student)
one third of the sum of three consecutive odd integers is 91. find the largest... (answered by CubeyThePenguin)
Find three consecutive odd integers such that the sum of the first integer twice the... (answered by mananth)