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 be x,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+11-11=74-11 [Subtracting 11 from both sides]
⇒ 9x+63
⇒ 9x/9=63/9 [Dividing both sides by 9]
⇒ x=7

Hence first integer = 7, second integer = 7 + 1 = 8 and third integer = 7 + 2 = 9.

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