Question

Three consecutive integers are such that when they are taken in increasing order and multiplied by 2, 3 and 4 respectively, they add up to 74. Find these numbers.

ps : whoever helps me i will give him brianliest

Answer 1

$\large{\underline{\underline{\textsf{{\red{Answer :- }}}}}}$

Let the three consecutive integers be x, x + 1 and x + 2.

As per the condition, we have

2x + 3(x + 1) + 4(x + 2) = 74

⇒ 2x + 3x + 3 + 4x + 8 = 74

⇒ 9x + 11 = 74

⇒ 9x = 74 – 11 (transposing 11 to RHS)

⇒ 9x = 63

⇒ x = 63 ÷ 9

⇒ x = 7 (transposing 7 to RHS)

Thus, the required numbers are 7, 7 + 1 = 8 and 7 + 2 = 9, i.e., 7, 8 and 9.

Answer 2

Answer:

Giνєn :

• ➤ Three consecutive integers are such that when they are taken in increasing order and multiplied by 2, 3 and 4 respectively.
• ➤ The sum of consecutive numbers is 74.

$\begin{gathered}\end{gathered}$

To Fiηd :

• ➤ The numbers

$\begin{gathered}\end{gathered}$

Concєpt :

» Here, the three consecutive integers are such that when they are taken in increasing order and multiplied by 2, 3 and 4 respectively, they add up to 74.

» So, let the consecutive numbers be x, (x+1), (x+2).

$\begin{gathered}\end{gathered}$

Solυtioη :

$\bigstar \: \underline{\underline{\sf{Here :-}}}$

★ The consecutive numbers are taken in increasing order and multiplied by 2, 3 and 4 respectively. So,

$\small{\longrightarrow{\sf{\pink{First \: consecutive \: number = 2x}}}}$

$\small{\longrightarrow{\sf{\pink{Second\: consecutive \: number = 3(x + 1)}}}}$

$\small{\longrightarrow{\sf{\pink{Third\: consecutive \: number = 4(x + 2)}}}}$

$\begin{gathered}\end{gathered}$

$\bigstar \: \underline{\underline{\sf{Now, According \: to \: the \: question:-}}}$

${\longrightarrow{\normalsize{\rm{\green{Sum \: of \: three \: consecutive \: numbers = 74}}}}}$

${\longrightarrow{\normalsize{\rm{\green{2x + 3(x + 1) + 4(x + 2)= 74}}}}}$

${\longrightarrow{\normalsize{\rm{\green{2x + 3x + 3 + 4x + 8= 74}}}}}$

${\longrightarrow{\normalsize{\rm{\green{(2x + 3x + 4x) + ( 3+ 8)= 74}}}}}$

${\longrightarrow{\normalsize{\rm{\green{9x+ 11= 74}}}}}$

${\longrightarrow{\normalsize{\rm{\green{9x= 74 - 11}}}}}$

${\longrightarrow{\normalsize{\rm{\green{9x= 63}}}}}$

${\longrightarrow{\normalsize{\rm{\green{x= \dfrac{63}{9}}}}}}$

${\longrightarrow{\normalsize{\rm{\green{x= \cancel{\dfrac{63}{9}}}}}}}$

${\longrightarrow{\normalsize{\underline{\underline{\rm{\green{x= 7 }}}}}}}$

∴ The value of x is 7.

$\begin{gathered}\end{gathered}$

$\bigstar \: \underline{\underline{\sf{Hence :-}}}$

✴ First consecutive number -

$\small{\dashrightarrow{\sf{\purple{2x}}}}$

$\small{\dashrightarrow{\sf{\purple{2 \times 7}}}}$

$\small{\dashrightarrow{\sf{\purple{14}}}}$

$\small{\dashrightarrow{\underline{\underline{\sf{\purple{First \: consecutive \: number = 14}}}}}}$

∴ First consecutive number is 14.

$\rule{200}2$

✴ Second consecutive number -

$\small\dashrightarrow{\sf{\purple{3(x + 1)}}}$

$\small\dashrightarrow{\sf{\purple{3(7 + 1)}}}$

$\small\dashrightarrow{\sf{\purple{3 \times8}}}$

$\small\dashrightarrow{\sf{\purple{24}}}$

$\small{\dashrightarrow{\underline{\underline{\sf{\purple{Second\: consecutive \: number = 24}}}}}}$

∴ Second consecutive number is 24.

$\rule{200}2$

✴ Third consecutive number -

$\small\dashrightarrow{\sf{\purple{4(x + 2)}}}$

$\small\dashrightarrow{\sf{\purple{4(7 + 2)}}}$

$\small\dashrightarrow{\sf{\purple{4 \times 9}}}$

$\small\dashrightarrow{\sf{\purple{36}}}$

$\small{\dashrightarrow{\underline{\underline{\sf{\purple{Third\: consecutive \: number = 36}}}}}}$

∴ Three consecutive number is 36.

$\begin{gathered}\end{gathered}$

Vєrificαtioη :

${\longrightarrow{\normalsize{\rm{\red{Sum \: of \: three \: consecutive \: numbers = 74}}}}}$

${\longrightarrow{\normalsize{\rm{\red{2x + 3(x + 1) + 4(x + 2)= 74}}}}}$

${\longrightarrow{\normalsize{\rm{\red{14 + 24 + 36= 74}}}}}$

${\longrightarrow{\normalsize{\rm{\red{14 + 60= 74}}}}}$

${\longrightarrow{\normalsize{\rm{\red{74= 74}}}}}$

${\longrightarrow{\normalsize{\underline{\underline{\rm{\red{LHS = RHS}}}}}}}$

Hence Verified!

$\begin{gathered}\end{gathered}$

Ansωєr :

• ➤ The three consecutive numbers are 14, 24 and 36.

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