[Copernicus]

the problem is posed as you are "paid 3 and paid 5" not you "win 3 and win 5", so unless the problem is worded poorly $1.23 is a better answer than $1.78.

Its like the old ploy of saying they are giving you 3 for 1, instead of 3 to 1 odds. In the latter the 3 is in addition to your stake, in the former it includes it.