Can anyone explain how to solve 'consecutive integer problems' ?

Question

imqwerty · Answer

okay i'll tell here better
  Right. The sum of three consecutive integers is 75. Find the largest integer.

qwertty123 · Answer

http://www.algebra.com/algebra/homework/word/numbers/Consecutive-Number-Word-Problems.lesson Here try this... Though it looks like @imqwerty is helping you just fine! :)

imqwerty · Answer

so we have 3 integers which are consecutive

remember that consecutive integers are like this-> $\color{red}a$ , $\color{red}{a}+1$ ,  $\color{red}{a}+2$ 

and any two consecutive integers differ by 1

imqwerty · Answer

okay till here?

anonymous · Answer

Yeah. Good so far

imqwerty · Answer

okay so we are given that the sum of 3 consecutive integers  is 75
so
1st we write 3 consecutive integers -
$a$ , $a+1$, $a+2$ 

and they u know that the sum of all these^ is 75
now try to make an equation from this information

anonymous · Answer

Wait, I dont quite know how to go about making it into an equation...

imqwerty · Answer

okay 1st of all-> is it clear that we are assuming the consecutive numbers to be-> $a$, $a+1$ and $a+2$ ?

anonymous · Answer

Yer. 
Is that with all them though? I mean, like if you had to find the sum of two it'd be x, x+1?

imqwerty · Answer

yes :)

imqwerty · Answer

okay so  the sum of our 3 consecutive numbers $x$, $x+1$ and $x+2$ will be this->

$\large (x) + (x+1) +(x+2)$
okay?

anonymous · Answer

Right, got it so far. Next you group like terms?

imqwerty · Answer

yes :)
try to group like terms and simplify

anonymous · Answer

3a+3=75 
Am I doing it so far? Or have I grouped wrong.

anonymous · Answer

Yer, now Im lost! 2+1=3... right?

imqwerty · Answer

oh sorry :/ u did that correct

qwertty123 · Answer

:)

imqwerty · Answer

so we have our equation-
$\large 3a+3=75$
try to find $a$ from here :)

anonymous · Answer

Haha, Its fine. 

So, I got a=24... ?

imqwerty · Answer

yes correct :)
$a$ was our 1st term and we have it
now the other terms we have to find are-> $x+1$ and $x+2$

anonymous · Answer

There's more? haha
So what are the other two variables for? I know what a was for, but not sure what this step is for.

imqwerty · Answer

aww i made a type ;-;
just replace that $x$ with $a$

imqwerty · Answer

*typo

anonymous · Answer

Another typo when saying you made a typo. ;) Lol

So how do I find the other terms??

imqwerty · Answer

a was our 1st term and we have it
now the other terms we have to find are-> $a+1$ and $a+2 $

now know what $a$ is
just put its value in $a+1$ and $a+2$ to get these terms

anonymous · Answer

Oh!! Right. So 24+1 and 24+2?

imqwerty · Answer

yes (B

anonymous · Answer

Okay... Uhm, not sure if im doing it right!
My work so far;
(24+1)+(24+2)
      25 + 26 = 75
               51 = 75 ?  XD

imqwerty · Answer

no no 
the question says->   
The sum of three consecutive integers is 75. $\color{red} {Find~ the~ largest ~integer~.}$

now we had these integers-> $a$ , $a+1$ and $a+2$
tell me which one is largest

anonymous · Answer

2?

imqwerty · Answer

wym by 2? :)
do you mean the 2nd one? this-> $a+1$ ?

anonymous · Answer

Oh, no I suppose I mean a+2

imqwerty · Answer

yes correct :)
now we had to find the largest integer
and we know that it is this-> $a+2$
we also know what is $a$
so can you find $a+2$ ?

anonymous · Answer

26?

imqwerty · Answer

yes :)
question=solved

anonymous · Answer

More than I thought It'd be haha

Thank you so much though, I actually understand it now thanks to you ;)

imqwerty · Answer

np :)