Question 1: The sum of three consecutive integers is forty two, find the three integers.
Solution:
Let \(x-1\), \(x\), and \(x+1\) are three consecutive integers
According to the given condition of question
\[\begin{align*} x-1+x+x+1&=42\\
3x&=42\\
x&=\frac{42}{3}\\
x&=14\\
\end{align*}\]
So, \(13\), \(,14\), and \(15\) are required numbers
——– Alternate Method ——–
Let \(x\), \(x+1\), and \(x+2\) are three consecutive integers
According to the given condition of question
\[\begin{align*} x+1+x+x+2&=42\\
3x+3&=42\\
3x&=42-3\\
3x&=39\\
x&=\frac{39}{3}\\
x&=13\\
\end{align*}\]
So, \(13\), \(,14\), and \(15\) are required numbers