SOLUTION: I need to write an algebraic expression for this word problem...The sum of three consecutive integers is 423. Find the integers.

Question 257577: I need to write an algebraic expression for this word problem...The sum of three consecutive integers is 423. Find the integers.
Found 5 solutions by shiela, dabanfield, stanbon, PRMath, Alan3354:
Answer by shiela(1)   (Show Source): You can put this solution on YOUR website!
First,write the equation
X+X+1+x+2=423
Next combine similar terms
3x+3=423
3x=423-3
3x=420
Divide all through out by 3
3x/3=420/3
The answer is 120
Answer by dabanfield(803)   (Show Source): You can put this solution on YOUR website!
The sum of three consecutive integers is 423. Find the integers.
Let x be the smallest of the three integers:
Then the next two consecutive integers are x+1 and x+2.
So we have:
x + (x+1) + (x+2) = 423
Solve for x. Then the other two integers are x+1 and x+2.
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
I need to write an algebraic expression for this word problem...The sum of three consecutive integers is 423. Find the integers.
-----------
Equation:
x-1 + x + x+1 = 423
3x = 423
x = 141
----
Integers:
x-1 = 140
x = 141
x+1 = 142
=================
Cheers,
Stan H.
Answer by PRMath(133)   (Show Source): You can put this solution on YOUR website!
I think the answer you were given by Sheila is not fully correct. The answer given to you by Stan H. is correct. Please use Stan's answer.
If your homework is to just write the algebraic expression, then yes, the answer from Sheila is correct.

If you have to SOLVE for the answer, then Sheila's answer is NOT correct. Please look at Stan's answer, but if you want to see where Sheila went wrong, just look at the following:

You were given this by Sheila:

First,write the equation
X+X+1+x+2=423 <--- This is correct.
Next combine similar terms
3x+3=423 <---- This is correct.
3x=423-3 <------ This is correct.
3x=420 <----- This is correct.
Divide all through out by 3 <---- This is correct.
3x/3=420/3 <---- This is correct.

The answer is 120 <<<------ THIS IS NOT CORRECT.

= 140. (420/3 DOES NOT equal 120)

Now if your FIRST number is indeed 140, then the next consecutive number will be 141 and the next consecutive number will be 142. Do these three numbers add to 423? Let's check:

140
141
142
_______
423 YES.

So to reiterate, Sheila gave you a good answer in terms of setting up the problem and maybe that was all you had to do for the work. However, if you had to solve the problem, the answer you were given was incorrect. Again, please follow Stan's answer. His explanation was excellent and will likely make very good sense to you.

I hope this helps you. :-)
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Do these the easy way:
423/3 = 141 which is the middle number.
--> 140, 141, 142

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