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Question 256845: I am homeschooling my teens.
One problem said, "Find three consecutive even integers whose sum is 108."
Okay so, Let X = 1st Integer
x + 2 = 2nd Integer
x + 4 = 3rd Integer
My problem is the next problem. It states...
"Find five consecutive odd integers whose sum is 85."
According to the Teachers Edition, it figures it the same way...
"Let X = 1st Integer
x + 2 = 2nd Integer
x + 4 = 3rd and so on
Shouldn't it be odd?
Let X = 1st Integer
x + 3 = 2nd Integer
x + 5 = 3rd and so on?
Of course, then it does not divide evenly. I am confused. How do you work an even problem the same way as on odd? Thank you for your help. A mom in need.
Belinda Esper
Found 2 solutions by richwmiller, Alan3354:
Answer by richwmiller(17219)   (Show Source):
You can put this solution on YOUR website! Generally it does not matter if you use n, n+2 for odd or even.
If it bothers you, you can use 2n+1 for an odd number.
Remember the letters are variables they stand for something but are not the numbers themselves until you put them in the problem.
Using n and n+1 for odd in one problem and even in the next is not much different that using x for 25 in one problem and 26 in another.
The variables take on the value of the problem.
n+n+2n+4=108
n+n+2+n+4+n+6+n+8=85
5n+20=85
5n=65
n=13
15
17
19
21
13+15+17+19+21=85
Now try it with your numbers
x+x+3+x+5+x+7+x+9
5x+24=85
5x=61=12.2
Just wrong
2n+1+2n+3+2n+5+2n+7+2n+9=85
10n+25=85
10n=60
n=6
Now the first odd number is 2n+1=26+1=13 same as in the problem you didn't like.
x+3+x+5+x+7+x+9+x+11=85
5x+35=85
5x=50
x=10
but our first number is x+3 =13
Now why did mine work and your didn't?
your first number was x and your second number was x+3 with a difference of 3
But what about your second and third numbers
x+3 and x+5 have a difference of two!
So your numbers are not all even nor all odd!
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! "Find three consecutive even integers whose sum is 108."
Okay so, Let X = 1st Integer
x + 2 = 2nd Integer
x + 4 = 3rd Integer
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Do these the easy way:
108/3 = 36, which is the middle number
--> 34, 36, 38
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Find five consecutive odd integers whose sum is 85.
Same here. 85/5 = 17
--> 13, 15, 17, 19, 21
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