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.

Given: 

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.

To do:

We have to find the numbers.

Solution:

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

According to the given question,

$2\times x+ 3\times(x+1) + 4\times(x+2) = 74$

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

$9x+11=74$

$9x = 74-11$

$9x = 63$

$x = \frac{63}{9}$

$x = 7$

$\Rightarrow x+1=7+1=8$

$x+2 = 7+2 =  9$

Therefore, the required numbers are $7, 8$ and $9$. 

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Updated on: 10-Oct-2022

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