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Question 12737: I need help please! The question I have is:
The sum of three consecutive odd integers = 171
Thank You!
Answer by glabow(165)   (Show Source):
You can put this solution on YOUR website! If you can solve basic equations, then I will guess that you don't see how to write the problem as an algebraic expression.
Three numbers add up to 171. They are consecutive odd integers. So first, how do you guarantee that you have an odd integer? If you just say x, it could be odd or even. But an even number plus 1 is always odd. So how do you guarantee that you have an even number? The answer is 2x. Whatever x is, 2x is even. If you add 1, the even number will become odd. So, 2x + 1 will always be an odd number.
What is the next odd number after 2x+1? Isn't it 2x+1 + 2? [Say, "yes."]
So two consecutive odd numbers would be 2x+1 and 2x+3. The next odd number would be 2x+5. The rest is easy.
(2x+1)+(2x+3)+(2x+5)=171
2x+2x+2x+1+3+5=171 [rearrange terms]
6x+9=171 [do the arithemetic; simplify the expression]
6x=162 [subtract 9 from both sides]
x=27 [divide both sides by 6]
2x+1= 2 * 27 + 1 = 55
Aha! the first odd number is 55!
The next two must be 57 and 59.
Do 55, 57, and 59 add up to 171?
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