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- anonymous

i have this one problem i have been working on all night. it is just beging algebra and was wondering if anyone could help...
Problem is..... four times the smallest of three consecutive odd integers is 236 more than the sum of the other two integers. Find the integers.

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- anonymous

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- anonymous

Let a,b,c be odd integers. Since the equation 2n+1 will always produce an odd value no matter what the value of n is (you can check if you really want to), then let a=2n+1, b=2n+3 (which will be the next odd number from a), and c=2n+5 (which will be the next odd number from b). Then we have:
4*a=236+(b+c)
Then we can use substitution.
4*(2n+1)=236+((2n+3)+(2n+5))
8n+4=236+(4n+8)
8n+4=244+4n
4n=240
n=60
So if we plug what we found n to be, we have
a=2(60)+1=121
b=2(60)+3=123
c=2(60)+5=125
I will admit that I probably would not have thought of this if I was in begining algebra (I actually had to stare at this question a little bit to see how to pull this off, besides just doing guess and check).
Please let me know if there is any step that does not make sense.

- anonymous

i think it makes perfect sense to me but that is not how my book says to do it so i did not try that way. when explaining consecutive odd integers it "any two consecutive odd integers differ by two. If x represents an odd integer, then (x+2) is the next larger odd integer." I was going to try it your way but thought it was wrong because of how they did a problem example as well. However, like I said your way was the way I wanted to do it the whole time but I thought it was the wrong way. Thank you for your time and help.

- anonymous

Well technically my way actually coincides with what your book's definition is. If you notice b is a(an odd number)+2, and c is b+2.

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- anonymous

But then again, I do not know how the problem example was done.

- anonymous

I see what you are saying. Here is the example problem and maybe you can help me see why I am getting confused.The sum of two consecutive odd integers is -188. Find the integers.
x + (x+2) = -188
2x + 2 = -188
2x + 2 -2 = -188 -2
2x = -190
2x div by 2= -190 div 2
x = -95
the first integer is x = -95
the second integer is x + 2 = -95 +2 =-93
the two integers are -95 and -93

- anonymous

what's the problem

- anonymous

x + (x+2) = -188 is this is a problem

- anonymous

no that is an example problem to illustrate how the book taught me. My problem is the word problem above.

- anonymous

Okay so with the route they are wanting to take, it will be similar to what I did except let's try it like this.
Let x represent an odd number (like how "a" was originally). Then
4*x=236+((x+2)+(x+2+2))
4*x=236+2+2+2+2x
4x-2x=236+6
2x=242
x=121
So x is the smallest. The next one will be 121+2=123, and the highest one will be 121+2+2=125. These are the same numbers.

- anonymous

i caan answer this question but DR. Pepper answered it first

- anonymous

nikkib0414 cm on chat box
please

- anonymous

ok thank you so much.... I see what I was doing wrong and that really helps. You have no idea how greatful I am. thank you again!!!!!

- anonymous

You're very welcome, nikkib.
Also, kushashwa, I am glad to hear you know how to answer this question.

- anonymous

dr. pepper i request u can u m in chat box

- anonymous

what is ordinary differential equation?

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