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.

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Solution

Let the three consecutive integers be $x, x + 1$ and $x + 2$ .
According to the question,
$\Rightarrow 2 x + 3 (x + 1) + 4 (x + 2) = 74$
$\Rightarrow 2 x + 3 x + 3 + 4 x + 8 = 74$
$\Rightarrow 9 x + 11 = 74$
$\Rightarrow 9 x = 63$
$\Rightarrow \frac{9 x}{9} = \frac{63}{9}$ [Dividing both sides by 9]
$\Rightarrow x = 7$
Hence first integer = 7, second integer = 7 + 1 =8 and third integer = 7+ 2= 9.

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Applications (Word Problem)

Standard VIII Mathematics

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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.

Let the three consecutive integers bex,x+1 and x+2. According to the question, ⇒2x+3(x+1)+4(x+2)=74 ⇒2x+3x+3+4x+8=74⇒9x+11=74 ⇒9x=63⇒9x9=639 [Dividing both sides by 9] ⇒x=7 Hence first integer = 7, second integer = 7 + 1 =8 and third integer = 7+ 2= 9.