The sum of three consecutive integers is 18, what are the numbers?

How to solve an algebra word problem about consecutive integers.

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TC Math Notes

[Anonymous-qw]

Let x be the first number.
Then x + (X+1) + (X+2) = 18
Then 3x + 3 = 18
Then 3x = 15; therefore x = 5
Therefore the numbers are 5, 6 and 7

[DarthFurie]

Before watching this video, the way I thought about it was 18 divided by 3 groups of about the same size, since all 3 numbers are consecutive. 18 ÷ 3 = 6, so I know my sequence has to have 6 in the middle so that the lower integer and the higher integer "balance" out to give me 2 more groups of 6. I can do this quickly in my head and get the solution "5, 6, and 7, " but I'm interested to watch the video and see how this could be solved algebraically

[robertarguello]

You know, ... it's problems like these that teach me the value Agebra! Thank you for introducing this problem. 👍

[danieldennis]

5, 6, 7 (x+y+z)=18 z=x+2 y=x+1 It's interesting that one almost automatically subconsciously creates a system of equations in one's head. This took a couple seconds to do and much longer to type. lo!

[ELREASON]

5, 6 & 7. Obviously 18\3=6 and then a one integer less (5) and the other an one integer more (7) also =18

[jeffreyabelson]

My set up: X + X + 1 + X + 2 = 18, so x = 5 (which checks!)

[argonwheatbelly]

5, 6, 7 in about 10 seconds in my head.

[jimmyrogers]

We did this in school many-many years as you explained it but when I first seen this, my thought was 18/3 =6 which was the middle number, so it was done 5 6 & 7. Do you still get the A+ if you cheat and get the right answer?😁

[Ricky_B]

5+6+7=18 the very first numbers that I thought of.

[tomtke]

since 18 is 3 × 6 then
6+5+4 won't work
but
7+6+5 will as 7 is 6+1 and 5 is 6-1

[jerryrowen]

I love you but talk talk talk talk talk talk talk talk talk talk talk

[kennethwright]

In ur head, 18/3 =6 so 6 is middle one : 5, 6, 7

[martinglenn]

Do you really think that there are people around that don't know what consecutive means, or are you just being patronising?