# RS-25E cost estimate but sentence confusing (approximately: help; maybe)?

So recently someone found out that the industry studies for SLS had been FOIAed by a site called government attic. While the other studies are interesting in their own right (check them out honestly), the United Space Alliance study (includes SX study as well) has a detailed analysis on various RAC concepts. It has a expansive list of engines for the first and second stage of SLS and while the information on engine unit and dev cost has been redacted for propriety reasons in the first stage engine table, there was a paragraph before that which states:

The RS-68B first flight engines would be available approximately at the same time as the RS-25E due to existing work already accomplished under the advanced Ares V engine development. A small amount of engine development cost on integrating the RS-68A would be required, and the recurring cost per engine set (five RS-25E versus four RS-68B) would be significantly more (approximately 90 percent per engine; approximately $165M per flight set) for the SSME derivative. This paragraph should provide a cost estimate for the RS-25E, however I have no clue on how to interpret it. (Originally I thought this was the source for the 40 mil a pop because 165/4 = ~40, but this is obviously wrong because there at 5 RS-25E for this stage) So how should this sentence be interpreted? • Thanks for posting those links! – Organic Marble Jan 22 at 0:35 ## 1 Answer the recurring cost per engine set (five RS-25E versus four RS-68B) would be significantly more (approximately 90 percent per engine; approximately$165M per flight set) for the SSME derivative.

Hey, it's one of those algebra word problems we trained for in school!

Obviously, I can't know how the author of this bit intended it, or if they made any errors, but my interpretation would be as follows:

Let $$x$$ be the cost of an RS-25E. Let $$y$$ be the cost of an RS-68B.

Take "...significantly more (90 percent per engine) for the SSME" to mean:

$$x = 1.9 y$$

Take "...significantly more ($165M per flight set) for the SSME" to mean: $$5 x = 4 y + 165$$ Convert $$x$$s to $$y$$s: $$=> 9.5 y = 4y + 165$$ Cancel: $$=> 5.5 y = 165$$ This would make the RS-68B \$30 million and the RS-25E \$57 million. My confidence in this interpretation is bolstered by the fact that the answers are in round millions! Your "40 mil a pop" reference notes that that figure comes from circa 2000, so an inflation to \$57M wouldn't be unreasonable for the 2011 USA study.

This Ars Technica story suggests that AJR will be getting \$100M per engine in the future.