Let the price of the hot dogs be x and drink be y.
It is given that you can get 6 hotdogsand 2 drinks for $18.00 so it follows:
[tex]6x+2y=18[/tex]Simplify to get:
[tex]3x+y=9\ldots(i)[/tex]It is also given that you can get 7 hotdogs and 8 drinks for $46.50 so it follows:
[tex]7x+8y=46.50\ldots(ii)_{}[/tex]Multiply (i) by 8 to get:
[tex]24x=8y=72\ldots(iii)[/tex]Subtract (ii) from (iii) to get:
[tex]\begin{gathered} 24x+8y=72 \\ - \\ 7x+8y=46.50 \\ 17x=25.5 \\ x=1.5 \end{gathered}[/tex]Substitute x=1.5 in (i) to get:
[tex]\begin{gathered} 3\times1.5+y=9 \\ y=4.5 \end{gathered}[/tex]Hence the cost are:
1.5$ per hotdog.
4.5$ per drink.