# EX.2.2 Q6 Linear Equations in One Variable Solutions - NCERT Maths Class 8

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## Question

Three consecutive integers add up to \(51\). What are these integers?

Video Solution

Linear Equations

Ex 2.2 | Question 6

## Text Solution

**What is known?**

Three consecutive integers add up to \(51\).

**What is unknown?**

Integers.

**Reasoning:**

Assume one integer to be a variable. Then use the property of consecutive integers and the given condition to form a linear equation.

**Steps:**

Let the first integer be *\(x\)*.

Then next consecutive two integers are \(x + 1\;{\rm{ and }}\;\,x + 2\)

\(x + (x + 1) + (x + 2) = 51\) [\(\therefore \) sum of the \(3\) consecutive integers is \(51\)]

\[\begin{align}3x + 3 &= 51\\3x &= 51 - 3\\3x &= 48\\x &= \frac{{48}}{3}\\x &= 16\\x + 1 &= 17\\x + 2 &= 18\end{align}\]

Three consecutive integers are \(16\), \(17 \) and \(18\).