Question

Four consecutive integers have the property that the sum of 16 less the first
number, 15 less than three times the second number, 4 more than the third, and
half of the fourth is 680. Find the integers.

Answer 1

Twice the sum of a number and three is the same as triple the difference of a number and two.

Answer 2

Call the numbers n, n+1, n+2 and n+3.
If we translate the sentences into algebra, we get:

16-n +
3(n+1) -15 +
n+2 +4 +
(n+3)/2 =

16-n+3n+3-15+n+6+0.5n+1.5=680

If you solve this equation, you have n, so you also have the other three numbers...