Question 102479: The sum of four consecutive odd integers is 216. Find the four integers.
Found 2 solutions by mjgulinello, Fombitz:
Answer by mjgulinello(10)   (Show Source):
You can put this solution on YOUR website! If you wanted to find four numbers that add up to 216, the easiest thing to do would be to divide 216 by 4. That would give you 54.
54 + 54 + 54 + 54 = 216
The key to this type of problem is that the four numbers we're looking for will have the same mean as the 4 numbers above, that is, 54.
Now to find two odd numbers with a mean of 54, all you do is add and subtract the same number to 54.
For example 54 - 1 = 53 and 54 + 1 = 55.
53 and 55 are consecutive odd integers with a mean of 54, that is they add up to 54 * 2.
Since we want four consecutive odd numbers we will also add and subtract 3.
54 - 3 = 51 and 54 + 3 = 57.
Now we have four consecutive odd numbers: 51, 53, 55, 57.
The mean is still 54, so they add up 54 * 4, or 216.
That's all for this problem.
-Mike
Answer by Fombitz(32388)  (Show Source):
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