SOLUTION: I cant figure out how to set up this problem: Find three consecutive odd integers whose sum is between 135 and 147

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Question 212940: I cant figure out how to set up this problem:
Find three consecutive odd integers whose sum is between 135 and 147
Found 2 solutions by Earlsdon, rapaljer:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Try this!
Let the three consecutive odd integers be:
(2x+1), (2x+3), and (2x+5). No matter what value x is, this will guarantee that the numbers are odd.
Now you can set up the inequality as shown:
135+%3C=+%282x%2B1%29%2B%282x%2B3%29%2B%282x%2B5%29+%3C=+147 Simplify.
135+%3C=+6x%2B9+%3C=147 Subtract 9 from all three sides(?).
126+%3C=+6x+%3C=+138 Now divide all by 6.
21+%3C=+x+%3C=+23 so the three consecutive odd integers are:
2x%2B1+=+2%2821%29%2B1=43
2x%2B3+=+2%2821%29%2B3=45
2x%2B5+=+2%2821%29%2B5=47

Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = first odd integer
x+2 = second
x+4 = third

The sum of these integers (add them up!) is 3x+6.

You must find x such that
135<3x+6<147

Bubtract 6 from the center, left, and right parts of this inequality:
135-6<3x+6-6<147-6
129<3x<141

Divide by 3:
129/3 43< x< 47

Now remember, x has to be an ODD NUMBER, BETWEEN (not including!) 43 and 47!!

So the first number must be x=45
The second number must then be x+2= 47
The third number is x+4 = 49

The solution: 45, 47, 49.
The sum is : 141

R^2

Dr. Robert J. Rapalje, Retired
Seminole Community College
Altamonte Springs Campus
Florida