A vendor sells h hot dogs and s sodas. If a hot dog costs twice as much as a soda, and if the vendor takes in a total of d dollars, how many cents does a soda cost?

Accepted Solution

Answer:[tex]Price\: of \:soda\: is:\:P_s= \frac{100d}{2h+s}[/tex]Step-by-step explanation:Let[tex]P_s = cost\: of\: soda[/tex][tex]P_h=cost \:of\:hotdog[/tex]in dollars.Then we know that[tex]P_h=2P_s[/tex]And if the vendor makes total of d dollars: [tex]hP_h+sP_s=d[/tex]Now substitute the value of [tex]P_h=2P_s[/tex] into this equation and get;[tex]2hP_s+sP_s=d[/tex][tex]=P_s(2h+s)=d.[/tex][tex]\therefore P_s= \frac{d}{2h+s}[/tex]Now this price is in dollars, and to convert it to cents we just multiply it by 100. [tex]\boxed{\therefore P_s= 100\frac{d}{2h+s} }[/tex]