Changing values in a distribution to match another

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this is my first question here.

I have a distribution of prices, let's say 10,000 values. I also have reference prices for all these 10,000 values. I want to change the values of my distribution in order to match the distribution of reference prices. For example my prices have an average of 200 coins, and the reference distribution's average is 150 coins.

The first option I tried was multiplying every price by an average factor corresponding to the percentage difference of the two averages. In the example, multiply all my 10,000 values by 0.75 would give me a new average of 150 coins.

That worked ok, but I have a further restriction that prevents me to using this option, which is:

The prices in my distribution that are below the reference prices can vary, but no too much.

One alternative I think could work is using a Min Max Scaler, but I'm not sure how that works.