FIND THE COST OF HOTDOGS AND HAMBURGERS

Question

At a concession stand, 

3 

hot dogs 

and 

4 hamburger(s) 

cost 

$13.25 

4 

hot dogs 

3 

hamburger 

$13.00 

Find the cost of one 

hotdog 

and the cost of one 

hamburge

Answer 1

Let's use d for # of hot dogs & h for # of hamburgers.

Here again, two unknowns require two equations.

You know the total cost for one combination of d & h, and a second combination of d & h, so you have the makings for both equations:

3d+4h=13.25

4d+3h=13.00

Use matrices, graphing, substitution, or elimination to solve for d & h. Be sure to check your solution in BOTH equations to be sure it's correct!

Answer 2

Whenever you have a question like this, you will need 2 equations.

One for each situation.

Since both of these start with the letter h, let's let hamBurger be represented by B and hot Dog be represented by D.

1st Situation: 3D + 4B = $13.25

2nd Situation: 4D + 3B = $13.00

Solve this system of equations. Multiply the top equation by (-4) and the bottom equation by (3), then we can add vertically and eliminate one of the variables.

-12D -16B = -53

12D +9B = 39

Adding vertically, the D's get eliminated.

-7B = -14

Divide both sides by -7, and find that B = 2

So one hamBurger costs $2.

Put B=2 back into the bottom (or top) equation to find that

4D + 3(2) = 13 or 4D + 6 = 13

Subtract 6 from both sides

4D = 7

Divide both sides by 4

D = 7/4 = 1.75

Do one hot dog costs $1.75

Cost of one hot dog and 1 hamburger = $1.75 + $2.00 = $3.75