SOLUTION: I need help with the following word problem. the sum of three consecutive odd numbers is 159. Find the three odd numbers.

Question 523381: I need help with the following word problem.
the sum of three consecutive odd numbers is 159. Find the three odd numbers.
Found 2 solutions by Alan3354, oberobic:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
159/3 = 53, the middle number
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Or,
(n-2) + n + (n+2) = 159, etc
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
Three consecutive odd numbers could be defined as x, y, and z.
But then you have 3 unkowns, so you need 3 equations to find a solution.
.
However, you know the numbers are consecutive odd numbers.
So, the first can be defined as 'x'.
That means the next two odd numbers is 'x+2' and 'x+4'.
Now you have only one unknown: 'x'.
.
And you know the sum of the three consecutive odd integers is 129.
.
If you were to have defined x + y + z = 129, then you would be stopped in your tracks.
.
But you've cleverly defined the numbers in terms of one unknown, 'x.'
So,
.
x +(x+2) +(x+4) = 129
.
3x +6 = 129
.
3x = 123
.
x = 41
.
Great! x is an odd integer!
.
x+2 = 43
x+4 = 45
.
Now we have three consecutive odd integers: 41, 43, and 45.
.
But check to ensure they total 129.
41+43+45 = 3*40 + (1+3+5) = 120 + 9 = 129
Correct.
.
Answer: The three consecutive odd integers that sum 129 are: 41, 43, and 45.
.
Done.
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