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First we need to understand that consecutive integers means integers such that each one is 1 bigger than the one before it. So 3 and 4 are consecutive.
Now if we let x be the first integer. The next is 1 bigger so it is x+1 and the third is 1 bigger than the second so it is x+2.
Now we are told the sum if 51 greater than the smallest number.

so we have x+x+1+x+2=3x+3=Sum
But we know that sum is 51 greater than x, so we write

3x+3=x+51
Solving we find:
2x=48
and x=24.
So the numbers are
24,25, and 26.
The sum is 75 which is 51 more than 24 so we are done.

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Q: Find three consecutive integers whose sum exceeds the smallest integer by 51?
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