Answer :
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:
[tex]S+H=220...(1)[/tex]If the number of sodas sold was 46 more than the number of hot dogs sold, we have:
[tex]S=46+H...(2)[/tex]Using equation (2) in (1):
[tex]\begin{gathered} 46+H+H=220 \\ 2H=220-46 \\ 2H=174 \\ \Rightarrow H=87 \end{gathered}[/tex]Finally, using this result in (2):
[tex]\begin{gathered} S=46+87 \\ \Rightarrow S=133 \end{gathered}[/tex]Answer: The vendor sold 133 sodas and 87 hot dogs.