There are 2 solutions. One where S is $1.10 and the other was S is 86 cents.
There was one other S has 76 cents. There are limited solutions because of the number of coins. And because there has to be 4 quarters.
It's just as I feared, then: ignoring the call of the question, encouraging students to think they've got the right answer when they haven't, and even supplying a wrong answer. Note that 76 cents for Stella is not a combination that fits the numeric relationships of the problem:
Stella could not have four quarters and a total less than a dollar. In addition, Stella could not have three quarters and a total of 76 cents, or she wouldn't have five coins. If she were to have two quarters, her maximum possible total would be 80 cents, but Joan would have two quarters as well, already boosting her well over half Stella's total; thus Stella could not have only two quarters. For similar and obvious reasons Stella could not have only one quarter or none.
ETA: (Were you looking at a solution given by the teacher, or just trying to reconstruct it yourself? The latter seems likely.)
The way this question was obviously set up was to give a sense of accomplishment after a bit of easy work. A coin combination that suits the numeric relationships was chosen to be likely to be explored first, as many of the students would want to first try the maximum possible total for Stella, $1.10, to give the most room for a half total for Joan, and because it makes sense to explore the space starting from the end.
Thus in essence it's really another of the many EM problems about adding up coins to a total, except this time it's simply adding up ten coins to 55 cents, and throwing in a false sense of accomplishment for having achieved something greater. It's the same old EM approach, but with extra elements added that will help to insure that many students wind up feeble-minded, happy creatures that can't even read a problem properly, and who quit at the first opportunity.
