The sum of four consecutive integers is decreased by 30, the result is the fourth integer. Find the four integers.

Answer 1

First represent the unknowns with variables. Note that the difference between two consecutive integers is one, so:
Let x = first integer
Let x+1 = second integer
Let x+2 = third integer
Let x+3 = fourth integer
Then we set up the equation by following the given condition.
x + x+1 + x+2 + x+3 - 30 = x+3
Then solve for x:
4x + 6 - 30 = x + 3
4x - 24 = x + 3
4x - x = 24 + 3
3x = 27
x = 9 (first integer)
x+1 = 10 (second integer)
x+2 = 11 (third integer)
x+3 = 12 (fourth integer)

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