Two consecutive integers are such that 3 times larger is 34 more than twice the smaller. What are the Integers?

Let x and y be two integers.

From the information they must satisfy the following:

x = y + 1 (two consecutive integers) EQN (1)

3x = 2y + 23 (2 times the smaller is 23 less than 3 times the larger) EQN (2)

Substituting (1) into (2) yields

3 (y+1) = 2y + 34

Solving gives us y = 31 and thus x = 32