What’s the answer to this problem

Question

At a concession stand, three hot dogs and two hamburgers cost $9.75; two hot dogs and three hamburgers cost $10.25. Find the cost of one hot dog and the cost of one hamburger.

Answer 1

Step 1: Define your variables

We are looking for the price of a hot dog and a hamburger so let "d" be the price of a hot dog and let "h" be the price of a hamburger.

Step 2: Write equations from the words

3d + 2h = 9.75

2d + 3h = 10.25

Step 3: Use one of the methods to solve the system of equations

Substitution:

If 3d + 2h = 9.75 then 2h = 9.75 - 3d and h = 4.875 - 1.5d

Now plug in "4.875 - 1.5d" into the second equation in place of "h":

2d + 3(4.875 - 1.5d) = 10.25

2d + 14.625 - 4.5d = 10.25

-2.5d = -4.375

d = 1.75

Using h = 4.875 - 1.5d then h = 4.875 - 1.5(1.75) = 4.875 - 2.625 = 2.25

So hot dogs are $1.75 and hamburgers are $2.25

Answer 2

Let:

Price of a hot dog - d

Price of a hamburger - h

System of 2 equations and 2 vars:

3d + 2h = 9.75

2d + 3h = 10.25

Solve whichever way you like. Substitute or multiply the first equation by 3/2 and substitute the second.

You will get that d = 1.75

And h = 2.25.