SOLUTION: Find four consecutive odd integers whose sum is 196

Question 110052: Find four consecutive odd integers whose sum is 196
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Call the first odd integer ... x
.
then the next odd integer is x + 2
.
the third consecutive odd integer is x + 4
.
the fourth consecutive odd integer is x + 6
.
Note that these show that the difference between consecutive odd integers is 2 ... think in
terms of 3, 5, 7, and 9 being consecutive odd integers and note that each is 2 away from
its predecessor.
.
If you add our 4 consecutive odd integers you get:
.
x + (x + 2) + (x + 4) + (x + 6) = 4x + 12
.
but you are told that this sum is 196. So set the sum equal to 196 and write it in the form
of an equation to get:
.
4x + 12 = 196
.
Get rid of the 12 on the left side by subtracting 12 from both sides to convert the equation to:
.
4x = 196 - 12 = 184
.
Then solve for x by dividing both sides by 4 to get:
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x = 184/4 = 46
.
What does this tell us? This cannot be an answer because the first number in the series is
an even number. Add up the 4 consecutive even integers ... that is add up 46 + 48 + 50 + 52
and you get 196 as the sum.
.
Try nearby odd numbers ... the sum of 45 + 47 + 49 + 51 equals 192. This is too small so the
series has to be "upped." Find the sum of 47 + 49 + 51 + 53 = 200. This is too big. So there
is no series of four consecutive odd numbers that will add to 196.
.
The conclusion is that this problem has no solution.
.
Hope this helps you to understand the problem and how to work on it.
.
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