Question

Q.2 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.

Answer 1

Answer:

The numbers are : 7, 8, & 9

Step-by-step explanation:

Step 1 : Suppose the numbers are :

• $x$
• $(x + 1)$
• $(x + 2)$

Step 2 : Express in increasing order :

$x$, $(x + 1)$ and $(x + 2)$

Step 3 : Numbers are multiplied by 2, 3, and 4 respectively :

$\to 2x$, $3(x + 1)$, $4(x + 2)$

$\to 2x$, $3x + 3$, $4x + 8$

Step 4 : Solving for $x$ :

Given that, after multiplied by 2, 3, and 4 they sums to 74.

${ \underline{ \boldsymbol{According \: to \: the \: question : }}}$

$\implies 2x + (3x + 3) + (4x + 8) = 74$

$\implies 2x + 3x + 3 + 4x + 8 = 74$

$\implies 9x + 11 = 74$

$\implies 9x = 74 - 11$

$\implies 9x = 63$

$\implies x = \dfrac{63}{9}$

$\implies x = 7$

$\therefore { \underline{\sf{The \: value \: of \: }}{ \underline{\boldsymbol{x \: {\sf{ is \: \bf 7}}}}}}$

Hence, the numbers are :

• $x = \bf 7$
• $(x + 1) = \bf 8$
• $(x + 2) = \bf 9$