Question

Sum of 3 consecutive integers is 33.Find the no.

Answer 1

$\textbf{\underline{\underline{Answer :-}}}$

$\text{First number = 10}$

$\text{Second Number = 11}$

$\text{Third number = 12}$

$\textbf{\underline{\underline{Explanation :-}}}$

Given :

Sum of the consecutive numbers = 33

Total Numbers = 3

To find :

The numbers

Solution :

Consider one number as x

Consider second number as x + 1

Consider third number as x + 2

Equation,

$\tt{\implies \: x + (x + 1) + (x + 2) = 33}$

$\tt{\implies \: x + x + 1 + x + 2 = 33}$

$\tt{\implies3x + 3 = 33}$

$\tt{\implies3x = 33 - 3}$

$\tt{\implies3x = 30}$

$\tt{\implies \: x = \dfrac{30}{3} }$

$\tt{\implies \: x = 10}$

${\boxed{\bigstar{\sf\:{x = 10}}}}$

${\boxed{\bigstar{\sf\:{First \: number = 10}}}}$

Value of x + 1

$\tt{\implies10 + 1}$

$\tt{\implies11}$

${\boxed{\bigstar{\sf\:{Second\: number = 11}}}}$

Value of x + 2

$\tt{\implies10 + 2}$

$\tt{\implies12}$

${\boxed{\bigstar{\sf\:{Third\: number = 12}}}}$

$\therefore$$\text{First number = 10}$

$\text{Second Number = 11}$

$\text{Third number = 12}$

$\textbf{\underline{\underline{Verification :-}}}$

$\tt{\implies \: x + (x + 1) + (x + 2) = 33}$

$\tt{\implies10 + (10 + 1) + (10 + 2) = 33}$

$\tt{\implies10 + 11 + 12 = 33}$

$\tt{\implies10 + 23 = 33}$

$\tt{\implies33 = 33}$

When we placed the value of x we got the required answer 33

${\boxed{\sf\:{LHS = RHS }}}$

$\therefore$$\text{First number = 10}$

$\text{Second Number = 11}$

$\text{Third number = 12}$