# 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 $$18$$.

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