Let S be the number of sodas sold, and H the number of hot dogs. If a vendor sold a combined total of 220 sodas and hot dogs, then:

If the number of sodas sold was 46 more than the number of hot dogs sold, we have:

Using equation (2) in (1):

Finally, using this result in (2):

Answer: The vendor sold 133 sodas and 87 hot dogs.