Question

the sum of three consecutive odd number is 177.find the number

Answer 1

Step-by-step explanation:

Consecutive odd integers means that an integer is skipped. The three integers are N, N + 2, and N + 4.

The set up equation is N + N + 2 + N + 4 = 177 Combine like terms

3N + 6 = 177 Subtract 3 to both sides to isolate N

3N + 6 - 6 = 177 - 6

3N = 171 Divide both sides by 3

3N/3 = 171/3

N = 57

N + 2 = 59

N + 4 = 61

57 + 59 + 61 = 177

57, 59, and 61 are the integers.

This method also works for consecutive even numbers.

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#pihu's answer

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,

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

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

$\implies 3x+3=177$

$\implies 3x = 177 -3$

$\implies 3x = 174$

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

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

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

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

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

$\large\textbf{Verification}$ :

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

$\textbf{Hence verified}$