Awoman bought 100 christmas cards. for the ones that sing a song when you open them, she paid 30 cents each. for the rest she paid 5 cents each. if the cards cost $10.25 in all, how many of the expensive kind did she buy?

.05c+.3s=10.25, c+s=100, c=100-s  (c is for cards that don't sing and s is for those that do :P)

.05c+.3s=10.25 and c=100-s makes the equation become:

.05(100-s)+.3s=10.25

5-.05s+.3s=10.25

.25s=5.25

s=21, and since c=100-s

c=79

So she bought 21 of the more expensive singing cards...