David did 56 more push-ups than Zachary in gym class today. If David did 38 push-ups how many push-ups did Zachary and David do altogether?
Let's denote David's number of push-ups by D and Zachary's number of push-ups by Z. 

Then we have: 

D = Z + 56 

Therefore we can solve for Z: 

Z = D - 56 

Now we can substitute Z in the original equation: 

D = (D - 56) + 56 

D = D 

Therefore we have: 

D + Z = D 

D = Z 

Now we can substitute D in the original equation: 

Z + 56 = D 

Z + 56 = Z 

56 = 0 

This is a contradiction.