Question

At a local baseball game, the concession stand has two different meal choices. You can get 6 hotdogsand 2 drinks for $18.00 or you can get 7 hotdogs and 8 drinks for $46.50. If the price of hotdogs anddrinks is the same for each meal, find how much it costs for an individual hotdog and how much itcosts for an individual drink.$per hotdog.$per drink.

Answer 1

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:

`6x+2y=18`

Simplify to get:

`3x+y=9\ldots(i)`

It is also given that you can get 7 hotdogs and 8 drinks for $46.50 so it follows:

`7x+8y=46.50\ldots(ii)_{}`

Multiply (i) by 8 to get:

`24x=8y=72\ldots(iii)`

Subtract (ii) from (iii) to get:

`\begin{gathered} 24x+8y=72 \\ - \\ 7x+8y=46.50 \\ 17x=25.5 \\ x=1.5 \end{gathered}`

Substitute x=1.5 in (i) to get:

`\begin{gathered} 3*1.5+y=9 \\ y=4.5 \end{gathered}`

Hence the cost are:

1.5$ per hotdog.

4.5$ per drink.