Question

Sum of three consecutive natural numbers is 177. Find the numbers.​

Answer 1

GIVEN:

Sum of three consecutive natural numbers = 177

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TO FIND:

The three natural numbers.

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SOLUTION:

$\bigstar {\sf {\pink {Let\ the\ first\ natural\ number\ be\ x}}}$

$\bigstar {\sf {\pink {Let\ the\ second\ consecutive\ natural\ number\ be\ (x+1)}}}$

$\bigstar {\sf {\pink {Let\ the\ third\ consecutive\ natural\ number\ be\ (x+2)}}}$

Now, we are given that sum of all the three numbers is 177.

So, the equation formed is,

x+(x+1)+(x+2) = 177

x+x+1+x+2 = 177

3x+3 = 177

3x = 177-3

3x = 174

$\sf x = \dfrac{174}{3}$

$\boxed {\bf {\red {x=58}}}$

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Verification:

On substituting the value of x as 58 in the equation,

x+(x+1)+(x+2) = 177

58+(58+1)+(58+2) = 177

58+59+60 = 177

177 = 177

LHS = RHS

Hence Verified!

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THE NUMBERS ARE:

• First number = x

= 58

• Second number = x+1

= 58+1

= 59

• Third number = x+2

= 58+2

= 60

$\boxed {\sf {\purple {The\ three\ consecutive\ natural\ numbers\ whose\ sum\ is\ 177\ are\ 58, 59\ and\ 60.}}}$

Answer 2

$\large\textbf{Given }$:

The sum of three consecutive natural numbers is 177.

$\large\textbf{To Find}$:

Find the three numbers

$\large\textbf{Solution}$:

Let x be the first number .

consecutive natural numbers will always have 1 as difference.

So , $x+1=2^nd\: \text{number ,}$$x+2=3^rd\:\text{number}$

It's given sum of three consecutive numbers is 177.

hence,

$\implies x+(x+1)+(x+2)=177$

$\implies x+x+x+1+2=177$

$\implies 3x+3=177$

$\implies 3x = 177 -3$

$\implies 3x = 174$

$\implies x = \frac{174}{3}$

$\implies \textbf {x\: = \: 3}$

$\implies x+1= 58+1 \implies \textbf{x+1=59}$

$\implies x+2=58+2 \implies\textbf{x+2=60}$

$\text{the three consecutive natural numbers is 58,59,60}$

$\large\textbf{Verification}$ :

$x+(x+1)+(x+2)=177\\x+x+x+1+2=177\\3x+3=177\\3(58)+3=177\\174+3=177\\177=177$

$\textbf{Hence verified}$