This was supposed to be a relatively easy puzzle that would get teams moving along to Manhunt before it got too dark. Because all of the coins in a set must have different values, this is basically a very simple Cross Sums puzzle. For instance, there are only two possibilities for the first set: 1 2 3 4 7 or 1 2 3 5 6. You could have either used the other constraints to eliminate the former or just flipped the sets over to see the word CABLE on one of them.
The correct sets are:
1 2 3 5 6 = CABLE
1 2 4 = CAR
3 4 6 7 = BREW
The cable car turnaround at Powell St. was nearby (we scrupulously cropped all other instances of the words "Cable Car" off of the map), and BREW was the answer word.
Incidentally, those were the same bubble gum coins that appeared in the "superhero supplies" in the Justice Unlimited Game.