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We are offering our product to you at the price of $20 (twenty dollars) per pound.

Wouldn't it be better to write

We are offering our product to you at a price of $20 (twenty dollars) per pound.

When googling, I seem to find both variants, and can't make out the difference.

The Google Ngram for "at the price of" vs. "at a price of" is puzzling too:

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    As this NGram which is more specific to your exact context shows, usage is somewhat flexible and preference varies over time. But both are fine, and I think it would be misguided to claim some nuance of difference. Commented Apr 3, 2016 at 16:17
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    I would say that "We are offering our product to you at $20 (twenty dollars) per pound" sounds more natural than adding "price".
    – zondo
    Commented Apr 3, 2016 at 16:35
  • @FumbleFingers Hmmm. What your Ngram seems to show is that the usage hardly differs at all! Virtually nobody uses either of these in writing (though no doubt they come up in speech). There are a maximum of two examples in each period for either one. So the arbitraty two-ness or one-nessor zero-ness of each example at any given period isn't statistically significant in any way. Commented Apr 3, 2016 at 17:25
  • Careful how you formulate your n-gram. You could also be counting sentences without numbers, like For a limited time, Lufthansa is offering round trips at the price of an equivalent EasyAir ticket. Commented Apr 3, 2016 at 17:29
  • @AlanCarmack - thank you. I felt like I had posted a question like this before, but a search for "at the price" gave no results, so I went ahead. Commented Apr 3, 2016 at 17:40

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While either is fine, I would prefer:

We are offering our product to you at a price of $20 (twenty dollars) per pound.

because there are various prices for a product (different stores, sales, etc.) and using a reflects this indeterminate nature.

I would use the when it is clear you are referring to the specific instance:

For the price of $20, we will also give you two tickets to the circus.

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