Question

The sum of four consecutive odd number is 216 find those numbers

Answer 1

Given : Sum of four consecutive odd numbers is 216

To find : Numbers

Solution :

Let the four consecutive odd numbers be n, n + 2, n + 4 and n + 6.

Now,

=> n + ( n + 2 ) + ( n + 4 ) + ( n + 6 ) = 216

=> 4n + 12 + 216

=> 4n = 216 - 12

=> 4n = 204

=> n = 204/4

=> n = 51

Therefore the required numbers are,

• n = 51
• n + 2 = 51 + 2 = 53
• n + 4 = 51 + 4 = 55
• n + 6 = 51 + 6 = 57

Hence the four consecutive terms whose sum is 216 are 51, 53, 55 and 57.

Answer 2

$\large\underline{\sf{Solution-}}$

Given that,

The sum of four consecutive odd numbers is 216.

We know,

↝ The two consecutive odd numbers differ by 2.

So, let assume that

$\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:\begin{cases} &\sf{First \: number \: = x} \\ \\ &\sf{Second \: number = x + 2}\\ \\ &\sf{Third \: number = x + 4}\\ \\ &\sf{Fourth \: number = x + 6} \end{cases}\end{gathered}\end{gathered}$

Now, According to statement, Sum of numbers is 216

$\rm \implies\:x + x + 2 + x + 4 + x + 6 = 216$

$\rm \implies\:4x + 12 = 216$

$\rm \implies\:4x = 216 - 12$

$\rm \implies\:4x = 204$

$\bf \implies\:x = 51$

Hence, Numbers are

$\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:\begin{cases} &\sf{First \: number \: = x = 51} \\ \\ &\sf{Second \: number = x + 2 = 51 + 2 = 53}\\ \\ &\sf{Third \: number = x + 4 = 51 + 4 = 55}\\ \\ &\sf{Fourth \: number = x + 6 = 51 + 6 = 57} \end{cases}\end{gathered}\end{gathered}$

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Basic Concept Used :-

Writing System of Linear Equation from Word Problem.

1. Understand the problem.

• Understand all the words used in stating the problem.

• Understand what you are asked to find.

2. Translate the problem to an equation.

• Assign a variable (or variables) to represent the unknown.

• Clearly state what the variable represents.

3. Carry out the plan and solve the problem.