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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.

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. 

Grade:12

1 Answers

Anand Kumar Pandey
askIITians Faculty 5693 Points
3 months ago
Dear Student

Let the three consecutive integers are 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=74–11
⇒9x=63
⇒x=63/9
⇒x=7
Thus, the numbers are: x=7
x+1=8 x+2=9

Thanks

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