Question

At a concession stand seven hot dog(s) and four ham burger(s) cost $14.00 , four hot dog(s) and seven ham burger(s)cost $16.25 . Find the cost of one hot dog and the cost of one hamburger What is the cost of the one hot dog ?

Answer 1

Let x=cost of hotdog

Let y=cost of hamburger ;

7x+4y=$14.00 ................(1)

4x+7y=$16.25 .................(2)

7x+4y=$14.00 Multiply this equation by 4

4x+7y=$16.25 Multiply this equation by 7

`\begin{gathered} 28x+16y=56 \\ (28x+49y=113.75)/(-33y=-57.75) \\ y=-(57.75)/(=33) \\ y=1.75 \end{gathered}`

sub the value of y in equ(1)

`\begin{gathered} 7x+4y=14 \\ 7x+4(1.75)=14 \\ 7x+7=14 \\ 7x=14-7 \\ 7x=7 \\ x=(7)/(7) \\ x=1 \end{gathered}`

Therefore the cost of one hotdog = $1 , and the cost of one hamburger = $1.75