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

Answer:

The cost of hamburger is $1.75.

The cost of hot dog is $1.25

Step-by-step 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