Don spent $2.36 for 22 stamps. If he bought only 10 cent stamps and 12 cent stamps, how many of each kind did he buy?

So for this problem I went through multiples of 12 that ended in 6, because that's the only way that you would get a 6 at the end of the total. With that I found that he would have to buy 8 of 12 cent stamps and the rest (14) ten cents stamps.