Question 8: The sum of three consecutive odd integers is \(51\). Find the three integers.
Solution:
Let \(x-2\), \(x\), and \(x+2\) are three consecutive odd integers
According to the given condition of question
\[\begin{align*} x-2+x+x+2&=51\\
3x&=51\\
x&=\frac{51}{3}\\
x&=17\\
\end{align*}\]
So, \(15\), \(,17\), and \(19\) are required numbers
——– Alternate Method ——–
Let \(x\), \(x+2\), and \(x+4\) are three consecutive odd integers
According to the given condition of question
\[\begin{align*} x+x+2+x+4&=51\\
3x+6&=51\\
3x&=51-6\\
3x&=45\\
x&=\frac{45}{3}\\
x&=15\\
\end{align*}\]
So, \(15\), \(,17\), and \(19\) are required numbers