What do you think of this recreational math problem?

There are a few classic recreational math problems that ask to find a counterfeit coin using a balance scale, knowing that the weight of the counterfeit is different from the others. For example, determine in two weighings which of 9 coins is heavier than the others.

Here is my addition to these problems. The country of East Fenwick has four coins, of value of $1, $5, $25 and $100. They all have the same weight.

Someone walks into your office with four bags, each one containing coins of one of the denominations. You are told that higher valued coins have been counterfeited. The higher valued coins all have the same weight, but they are heavier than the lower valued coins. The person leaves abruptly without telling you where the division is between lower and higher valued coins.

Assuming that what you have been told is true, determine which of the coins are counterfeit in one weighing of the balance.