# word problem help

• Aug 27th 2012, 03:27 PM
krrice
word problem help
Hi everyone, I have a word problem that I am trying to help my son with any information will be greatly appreciated.

Find three consecutive odd integers such that the second is at most three less than twice the sum of the first and third.

He needs the equation they gave him -1 , 1, 3
• Aug 27th 2012, 05:04 PM
Soroban
Re: word problem help
Hello, krrice!

Quote:

Find three consecutive odd integers such that the second
is at most three less than twice the sum of the first and third.

He needs the equation.
They gave him -1 , 1, 3. . Is that the answer?
There is more than one answer.

Let the three consecutive odd integers be: . $x,\,x\!+\!2,\,x\!+\!4$

$\underbrace{\text{Second}}_{x+2}\; \underbrace{\text{is at most}}_{\le}\;\underbrace{\text{twice}}_{2\;\times } \;\underbrace{\text{sum of first and third}}_{x+(x+4)}\;\underbrace{\text{minus 3}}_{-\;3}$

We have: . $x+2 \;\le\;2\big[x+(x+4)\big] - 3$

. . . . . . . . $x + 2 \;\le\;4x + 8 - 3$

. . . . . . . . . $-3x \;\le \; 3$

. . . . . . . . . . . $x \;\ge\;-1$

So, $[-1,1,3]$ is a solution.

But so are: . $\begin{Bmatrix}[1,3,5] \\ [3,5,7] \\ [5,7,9] \\ \vdots \end{Bmatrix}$