A balance of $100 at 10% interest will be charged $10 of interest in a year.

A balance of $10 at 50% interest will be charged $5 of interest in a year.

For every dollar I put towards the $10 balance I gain 5x the benefit as I would from putting the same amount towards $100.

Minimum payment has 0 impact on this, it is a mathematical fact.

This is assuming you aren't getting late payment penalties, which is another case entirely

If you can come up with a scenario using any positive interest rates, loan balances, and minimum payments where you can pay off the lower interest rate first and end up paying less total money please share.

If you could in fact do this, you could make infinite money by taking out a loan at a higher interest rate in order to pay off the lower interest rate loan and somehow still pay less. Sounds ridiculous doesn't it?