To solve this problem, we can turn it into an algebraic equation.

Let x be the lighter dog. Since the heavier dog is 25 lbs heavier than the lighter dog, we can express him/her as x+25. The two dogs' weight added up is 137 lbs, so our initial equation will be x+(x+25)=137. Since addition is associative, our equation will now simplify to 2x+25=137. We can now isolate the variable by subtracting 25 on both sides, which gives us 2x=112. Then dividing 2 by both sides gives us x=56. Since x is the weight of the lighter dog, the lighter dog is 56 lbs. The heavier dog is 25 lbs more heavier than the lighter dog, so the heavier dog is 56 lbs+ 25 lbs= 81lbs.

Hope this helps! If I messed something up, please let me know. Have a nice day!