Question

The sum of four consecutive odd numbers is 128.find the numbers
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Answer 1

Given:

• Sum of four consecutive odd numbers is 128.

To Find:

• The numbers

Required Solution:

Let four consecutive odd numbers be:

• 2x + 1
• 2x + 3
• 2x + 5
• 2x + 7

According to the Question,

(2x + 1) + (2x + 3) + (2x + 5) + (2x + 7) = 128

➟ 8x + (1 + 3 + 5 + 7) = 128

➟ 8x + 16 = 128

➟ 8x = 128 – 16

➟ 8x = 128

➟ x = 128/8

➟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀x = 14

So,

• 2x + 1 = (2 × 14) + 1 = 29
• 2x + 3 = (2 × 14) + 3 = 31
• 2x + 5 = (2 × 14) + 5 = 33
• 2x + 7 = (2 × 14) + 7 = 35

Hence, The required numbers are:

• 29
• 31
• 33
• 35

Answer 2

$\normalsize{\underline{\underline{\bf{Given:}}}}$

$\:\:\:\:\normalsize\bullet{\sf{The\:sum\:of\:four\: consecutive\:numbers\:is\:128.}}$

$\:\:\:\:\normalsize\bullet{\sf{And\:the\:four\: consecutive\:numbers\:are\:odd.}}$

$\normalsize{\underline{\underline{\bf{Need\:to\:find:}}}}$

$\:\:\:\:\normalsize\bullet{\sf{The\:four\:numbers.}}$

$\normalsize{\underline{\underline{\bf{Solution:}}}}$

$\normalsize{\sf{Let,\:the\: four\:numbers\:be:}}$

• $\normalsize{\tt{\red{(2x+1)}}}$
• $\normalsize{\tt{\red{(2x+3)}}}$
• $\normalsize{\tt{\red{(2x+5)}}}$
• $\normalsize{\tt{\red{(2x+7)}}}$

$\normalsize{\sf{According\:to\: the\: given\:question,}}$

$\:\:\:\normalsize{\tt{(2x+1)+(2x+3)+(2x+5)+(2x+7)=128}}$

$\normalsize\implies{\mathrm{8x+16=128}}$

$\normalsize\implies{\mathrm{8x=128-16}}$

$\normalsize\implies{\mathrm{8x=112}}$

$\normalsize\implies{\mathrm{x=\cancel{\frac{112}{8}}}}$

$\:\:\:\normalsize\implies{\boxed{\tt{x=14}}}$

$\normalsize{\sf{By\: substituting\:the\:value\:of\:x,}}$

$\normalsize\longrightarrow{\tt{(2x+1)=(2\times14+1)=28+1=\red{\underline{29}}}}$

$\normalsize\longrightarrow{\tt{(2x+3)=(2\times14+3)=28+3=\red{\underline{31}}}}$

$\normalsize\longrightarrow{\tt{(2x+5)=(2\times14+5)=28+5=\red{\underline{33}}}}$

$\normalsize\longrightarrow{\tt{(2x+7)=(2\times14+7)=28+7=\red{\underline{35}}}}$

$\normalsize{\underline{\underline{\bf{Verification:}}}}$

$\normalsize{\sf{Sum\:of\: obtained\:numbers=128}}$

$\normalsize\rightarrow{\mathbb{29+31+33+35=128}}$

$\normalsize\rightarrow{\mathbb{60+68=128}}$

$\normalsize\rightarrow{\mathbb{128=128}}$

$\normalsize\rightarrow{\sf{L.H.S=R.H.S}}$

$\normalsize\rightarrow{\sf{Hence,\: verified!}}$

$\normalsize{\underline{\underline{\bf{Final\:answer:}}}}$

$\footnotesize\therefore\underline{\boxed{\tt{\pink{The\:four\: consecutive\:odd\:numbers\:are\:\:29,\:31,\:33\:and\:35.}}}}$

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