SOLUTION: The sum of four consecutive odd integers is 112. What is the greatest of the four integers?

Question 18423: The sum of four consecutive odd integers is 112. What is the greatest
of the four integers?
Found 2 solutions by Alwayscheerful, mmm4444bot:
Answer by Alwayscheerful(414) (Show Source): You can put this solution on YOUR website!
You probably are thinking "I need to find 4 numbers, I need 4 variables." Not quite. Since they are consecutive and odd, you only need 1 variable.
Let's use N as the variable.
Pretend N=3. The next odd integer is 5. What is the difference? 2.
So, you can use the variables
N, N+2, N+4, N+6
Those will give you your consecutive odd.
Then just make them into a mathamatical equation

Since you got 1 number, you got all 4.
25 is the smallest of the 4 numbers, so just add 6 to get your final answer.

31 is your greatest.
Hope this helps!
Answer by mmm4444bot(95) (Show Source): You can put this solution on YOUR website!
Hello There:
Consecutive odd integers always differ by 2, so if we choose x to be the smallest of the four, then we can write the following expressions for the four consecutive odd integers:
x
x + 2
x + 4
x + 6
This leads to the following equation:
x + x + 2 + x + 4 + x + 6 = 112
Simplify the left side:
4x + 12 = 112
Solve for x:
4x = 100
x = 25
Our four integers are: 25, 27, 29, 31.
So, the answer is 31.
(Check to verify that these integers add up to 112.)
~ Mark

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