That's not a very good comparison, because she did almost everything she could possibly do to try to run up the price.

She was offered a settlement before she was sued of under $3/song (she pirated 1700 songs and the RIAA asked for $5000). When she would not settle, they picked 24 of the 1700 songs and actually filed suit for statutory damages. Why 24, instead of all 1700? I'll cover that at the end.

Statutory damages range from $750 per infringed work to $30000. If the defendant can prove she was an "innocent infringer", the low end drops to $200 per infringed work. An innocent infringer is an infringer who did not know and had no reason to believe they were infringing. If the infringement is willful, the high end can go up to $150000. The actual amount within that range is determined by the jury.

Since she was in fact guilty, and should have easily known she had almost no chance of winning at trial, and almost no chance of convincing anyone she was an innocent infringer. It is then a simple matter or arithmetic to conclude that going to trial is in the best realistic case going to result in a minimum of $18000 damages. This is the point where those who are not massively stupid say "I'd like to accept your settlement offer now".

As I said, the actual amount of damages awarded is determined by the jury. She had tried to destroy evidence, she was caught in outright lies on the stand, and she tried to blame her children and boyfriend for the infringement. This probably made the jury less likely to head down to $750 per work, and they ended up at $9000 per work.

Why sue over just 24 songs, instead of all 1700?

Contrary to popular belief, they aren't setting out to ruin people's lives. When they catch a pirate and make a settlement offer, they offer a very reasonable amount, typically around $2-4 per infringed song, which comes out in most cases to a few thousand dollars. This is large enough to be annoying and serve as a discouragement to others, but not so large in most cases to seriously mess up one's life for a long time.

If they cannot get a settlement and it goes to trial, they cannot ask for $2-4 per song. That's below the minimum possible statutory damages award. If they sued over all 1700 songs in the Thomas-Rasset case, for instance, a win would result in a minimum award of $1.3 million, and probably much much more. Since they will be happy with a much smaller amount, they can cut down on the number of songs and still achieve their goals.

Also, there is a cost to including a song in the lawsuit. For each song, they need to make sure it was properly registered with the copyright office, and show that they are authorized by the copyright owner to sue on his behalf. The court will know about the settlement offer and so will know what kind of damages the plaintiff finds acceptable, and might get annoyed if it perceives them as just piling on. You do not want to annoy the court.

I don't know how they came up with specifically 24. 7 would be enough at $750 per song to get the $5000 they were initially looking for. Toss in a few more to allow for the possibility that the defendant will be able to find some flaw in the paperwork or in the RIAA's right to act on behalf of the copyright holder on some of them. Maybe they now want more than $5000 because their collection costs have risen in this case from "write a letter" costs to "prepare a lawsuit" costs.

Or it could be that a list of 7 songs (enough to get the $5000 they want) just looks small. Perhaps they believe a jury will think "why are they wasting our time over a measly 7 songs?" and so go with a beefier list.