Question

The sum of three consecutive natural numbers is 606, find the numbers.
The three numbers in increasing order are ___,___ and ___

Answer 1

The sum of three consecutive integers is 18, find the numbers.

Just in case you didn't know, \(«\)integers\(»\) are numbers from \(1\) and on ...
The few first integers are: \(1\), \(2\), \(3\), \(4\), \(5\), \(6\), \(7\), \(...\)

So, you can let your first integer to be \(x\),
and you can write the sum of three consecutive integers as:
\(\color{#000000}{ \displaystyle x+x+1+x+2 }\)

and sicne you know that the sum of three consecutive integers i equal to 18, you can write the following equation.
\(\color{#000000}{ \displaystyle x+x+1+x+2=18 }\)

If you add like terms, you get,
\(\color{#000000}{ \displaystyle 3x+3=18 }\)

Then, you can solve this for \(x\).
(Rememeber that \(x\) is your first integer.
\(\color{#000000}{ \displaystyle 3x+3=18 }\)
\(\color{#000000}{ \displaystyle 3x+3\color{red}{-3}=18\color{red}{-3} }\)
\(\color{#000000}{ \displaystyle 3x=15 }\)
\(\color{#000000}{ \displaystyle 3x\color{red}{\div3}=15\color{red}{\div3} }\)
\(\color{#000000}{ \displaystyle x=5 }\)

So, your first integer is \(5\), and thus the other following two are: \(6\) and \(7\). NOTICE, that indeed \(5+6+7=18\).