45 ducks and rabbits in the same cage, 146 feet. How many ducks and rabbits are there?

This question is for 45 ducks and rabbits. Assuming all 45 rabbits, there should be 180 feet. This question only tells us that there is 146 feet, and my calculated 180 feet is 34 feet more than the actual one. This is because 1 duck has two feet, but we regard it as four. If you replace 1 duck with 1 rabbit, you will lose two feet. So, how many two feet are included in 34 feet, that is, how many ducks we regard as rabbits. Obviously, 34 ÷ 2 = 17 (only). So there are 17 ducks and 28 rabbits.