Here's how to do it using algebra:
Let the smaller integer be 'x' . Then the larger integer is (x+1).
Their sum is (x) + (x+1).
That's (2x + 1) .
The problem says their sum is 73, so we can write . . . 2x + 1 = 73 .
Subtract 1 from each side . . . 2x = 72
Divide each side by 2 . . . x = 36
The smaller integer is 36 .
The larger integer is (x+1) . That would be 37.
The two consecutive integers are 36 and 37 .
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Here's how to do it using your brain:
-- If they were both the same number, then their sum would be double it, and each integer would be half of 73 .
-- That's 36.5 .
-- But 36.5 is not even an integer, so neither integer can be 36.5. Is there something we can do to a pair of 36.5s to make them whole numbers (integers), make them different, and make them consecutive, but not let their sum change ?
-- Well, if we slice off a piece from one of them and glue it onto the other one, then we'll wind up with two numbers that are different, and their sum won't change.
-- What happens if we take the .5 off of one of them and glue it onto the other one ? Then one of the 36.5s shrinks to become 36, and the other one grows to become 37 .
-- Well whaddaya know ! Now we have two numbers that are consecutive integers, and they add up to 73 . Great move !