Question

At a concession​ stand, seven hot dog (s )and two hamburger (s )cost ​$12.25​; two hot dog (s )and seven hamburger (s )cost ​$14.75. Find the cost of one hot dog and the cost of one hamburger.

Answer 1

The cost of hamburger is $1.75.

The cost of hot dog is $1.25

Explanation:

Consider the provided information.

Seven hot dog (s )and two hamburger (s )cost ​$12.25​;

Let the cost of hot dog is x.

The cost of hamburger is y.

Therefore,

`7x+2y=12.25`......(1)

Two hot dog (s )and seven hamburger (s )cost ​$14.75.

`2x+7y=14.75`......(2)

Use elimination method to solve the above equation.

Multiply equation 1 by 2 and multiply equation 2 by 7 and subtract them as shown:

`\ \ \ 14x+4y=24.5\\-14x-49y=-103.25\\\overline{\ \ \ \ \ \ \ \ \ \ \ \ \ 45y=78.75}`

`y=1.75`

Hence, the cost of hamburger is $1.75.

Now substitute the value of y in equation 1.

`7x+2(1.75)=12.25`

`7x+3.5=12.25`

`7x=8.75`

`x=1.25`

Hence, the cost of hot dog is $1.25