17. michelle spent $32 on hot dogs and hamburgers. hot dogs were $5 and hamburgers $6. if she bought a total of 6 items, how many of each kind did she buy?

I am not sure if this is the only answer but i used trial and error to work this out.
I first calculated 6x 4= 24, meaning 4 hamburger. But that one left me with $8 left which would not work as each hot dog is $5 each. So the answer i got was:
4 hot dogs at $5 equals $20.  2 hamburgers equals $12. so all together, 20 plus 12= $32.