Each pack of hot dogs contains 10 hot dogs (no buns), but each pack of hot dog buns contains 8 buns. phil buys a number of these packs for a barbecue. after the barbecue, phil finds that he has 4 hot dogs left over. what is the second smallest number of packs of hot dogs he could have bought?

Hmmm

we might need to find greatest common denomenator?
or we could just do trial and error

hmm

wait a minute

lets do this
d=number of hot dog packs
b=number of hot dog bbuns

the number of hot dogs is 4 more than the number of buns
10d=4+8b
divide both sides by 2 to make it easier
5d=2+4b

one way is to do trial and error

try values of d and find what values work for b (remember, all whole values)
if d=1, no value works for b
if d=2, b=2
that is the smallest value
keep going up
if d=3, no value works for b
if d=4, no value works for b
if d=5, no value works for b
if d=6, b=7

so 6 packs is the answer