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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 :

Solution

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

[tex]\begin{gathered} 28x+16y=56 \\ \frac{28x+49y=113.75}{-33y=-57.75} \\ y=-\frac{57.75}{=33} \\ y=1.75 \end{gathered}[/tex]

sub the value of y in equ(1)

[tex]\begin{gathered} 7x+4y=14 \\ 7x+4(1.75)=14 \\ 7x+7=14 \\ 7x=14-7 \\ 7x=7 \\ x=\frac{7}{7} \\ x=1 \end{gathered}[/tex]

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

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