SOLUTION: Find four consecutive odd integers whose sum is 296. Enter your answer as a list of numbers separated by a comma: a,b,c,d

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Question 1202564: Find four consecutive odd integers whose sum is 296.
Enter your answer as a list of numbers separated by a comma: a,b,c,d
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
Consecutive four odd integers, n-3, n-1, n+1, n+3

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The two odd integers surrounding this are 73 and 75.
..
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----original solution was very wrong----


Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!
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Find four consecutive odd integers whose sum is 296.
Enter your answer as a list of numbers separated by a comma: a,b,c,d
~~~~~~~~~~~~~~~~


        The solution in the post by @josgarithmetic,  giving the answer  145,  147,  149,  151,  is  INCORRECT,
        as anybody can check by adding these numbers.

        I came to bring you a correct solution. 


Let n be the smallest of the four consecutive odd integer numbers.

Then the numbers are

    n, (n+2), (n+4), (n+6).


Their sum is 296, so we write this equation

    n + (n+2) + (n+4) + (n+6) = 296.


Simplify this equation and find n

    4n + 12 = 296

    4n = 296 - 12

    4n = 284

     n = 284/4 = 71.


The numbers are 71, 73, 75 and 77.    ANSWER


CHECK.  71 + 73 + 75 + 77 = 296.    ! correct !

Solved (correctly).



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