4.3 Systems of Linear Equations and Problem Solving

Question

At a concession stand, five five hot dog left parenthesis s right parenthesis hot dog(s) and two two hamburger left parenthesis s right parenthesis hamburger(s) cost $ 10.25 10.25; two two hot dog left parenthesis s right parenthesis hot dog(s) and five five hamburger left parenthesis s right parenthesis hamburger(s) cost $ 12.50 12.50. Find the cost of one hot dog hot dog and the cost of one hamburger hamburger.

Answer 1

Hi, Deja.

Ok. So let's call:

d = price of hotdogs

h = price of hamburgers

5d +2h = 10.25

2d +5h = 12.50

 

let's multiply the  first equation by 2:

10d + 4h = 20.50

 

Let's multiply the 2nd equation by 5:

10d + 25h = 62.50

Now we can subtract the equations.

 

10d + 25h =  62.50

-10d + -4h = -20.50

 

21h = 42

h = 2.00

Now, substitute back into first equation:

5d + 2(2.00) = 10.25

5d + 4.00 = 10.25

5d = 6.25

d = 1.25

 

So, hamburgers cost $2.00

and hotdogs cost $1.25