Question

At a concession stand five hot dogs and four hamburgers cost $12 for hot dogs and five hamburgers cost 1275 the cause of one hot dog in the cost of one hamburger

Answer 1

The cost of one hot dog $1 and the cost of one hamburger is $1.75.

Explanation:

Given:

At a concession stand five hot dogs and four hamburgers cost $12.

Four hot dogs and five hamburgers cost $12.75.

Now, to find the cost of one hot dog and the cost of one hamburger.

Let the cost of one hot dog be
`x.`

And let the cost of one hamburger be
`y.`

So, the cost of five hot dogs and four hamburgers:

`5x+4y=12\\\\`

`4y=12-5x`

Dividing both sides by 4 we get:

`y=3-(5x)/(4)` .......(1)

And, the cost of four hot dogs and five hamburgers:

`4x+5y=12.75`

Substituting the value of
`y` from equation (1):

`4x+5(3-(5x)/(4))=12.75`

`4x+15-(25x)/(4)=12.75`

`4x-(25x)/(4)+15 =12.75`

`(16x-25x)/(4)+15=12.75`

`(-9x)/(4) +15=12.75`

Subtracting both sides by 15 we get:

`(-9x)/(4)=-2.25`

Multiplying both sides by 4 we get:

`-9x=-9`

Dividing both sides by -9 we get:

`x=1.`

The cost of one hot dog = $1.

Now, substituting the value of
`x` in equation (1):

`y=3-(5x)/(4)`

`y=3-(5* 1)/(4)`

`y=3-(5)/(4)`

`y=3-1.25`

`y=1.75.`

The cost of one hamburger = $1.75.

Therefore, the cost of one hot dog $1 and the cost of one hamburger is $1.75.