At a concession stand, three hot dog (s) and two hamburger (s) cost $6.50 ; two hot dog (s) and three hamburger (s) cost $7.25. Find the cost of one hot dog and the cost of one hamburger.

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

Step-by-step explanation:

We are going to make 2 equations with which the problem tells us

h = hamburger cost

d = hot dog cost

3d + 2h = $6.50

3h + 2d = $7.25

we clear the h in the first equation

3d + 2h = $6.50

2h = 6.50 - 3d

h = (6.50 - 3d) / 2

h = (6.50 - 3d) / 2

h = (3.25 - 3/2 d)

we replace the value of h in the second equation by (3.25 - 3/2 d)

3h + 2d = $7.25

3 (3.25 - 3/2 d) + 2d = $7.25

9.75 - 9/2 d + 2d = 7.25

- 9/2 d + 2d = 7.25 - 9.75

-5/2 d = - 2.5

d = - 2.5 / (-5/2)

d = 1

we replace the value obtained from d in the first equation

h = (3.25 - 3/2 d)

h = (3.25 - 3/2 * (1))

h = 3.25 - 1.5

h = 1.75

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