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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.

Q.8 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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Let the consecutive integers be x, x+1, x+2.

Now according to the question equation becomes, 

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

 or         2x + 3x + 3 + 4x + 8 = 74

 or             9x + 11 = 74

Transposing 11 to the RHS we get, 

        9x = 74 - 11 = 63

Divinding both sides by 9.

 x = \frac{63}{9} = 7

Therefore required consecutive integers are 7, 8, 9.

 

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