Question

At a concession stand, five hot dogs and two hamburgers cost $11.75; two hot dogs and five hamburgers cost $11.00. How do you find the cost of one hot dog and the cost of one hamburger?

Answer 1

`"Price of one hotdog"=1.75$`
`"Price of one hamburger"=1.5$`

Explanation:

`"Price of one hotdog"=x`
`"Price of one hamburger"=y`

1. `5*x+2*y=11.75`
2. `2*x+5*y=11.00`

From first equation we find y in terms of x:
`5*x+2*y=11.75`
`2*y=11.75-5*x`
`y=(11.75-5*x)/2`

Putting the value of y in the second equation:
`2*x+5*y=11.00`
`2*x+5*(11.75-5*x)/2=11.00`

We multiply the whole equation by 2 to get ride of the fraction:
`(2*x+5*(11.75-5*x)/2=11.00)*2`
`2*2*x+5*cancel2(11.75-5*x)/cancel2=11.00*2`
`4*x+5(11.75-5*x)=22.00`

`4*x+58.75-25*x=22.00`

Subtracting 58.75 from both sides of the equation we get:
`4*x+cancel58.75-25*xcancel(-58.75)=22.00-58.75`
`-21*x=-36.75`

Multiplying the whole equation by -1 we get:
`(-21*x=-36.75)*-1`
`21*x=36.75`

Dividing both sides by 21 to isolate x, we get:
`cancel21x/cancel21=36.75/21=1.75$`

Substituting the value of x in equation of y we get:
`y=(11.75-5*x)/2=(11.75-5*1.75)/2=1.5$`

`rArr "price of one hotdog"=x=1.75$`
`and "price of one hamburger"=y=1.5$`