At a concession stand, three hot dogs and four hamburgers cost $ 14.25 and four hamburgers and three hot dogs cost $13.75. find the cost of one hamburger and one hot dog.

I commented on your question but I'll solve it as if the second scenario had 4 hot dogs and 3 hamburgers totaling $13.75

Let D represent hot dogs. Let H represent hamburgers.



This is called a system of equations.  You must substitute one equation into the other.  I'll work it through, and hopefully you can follow along.



Now you have the value of one hot dog (D).  Substitute this value into the other equation. This way you will only be working with the H variable.



9/4=2.25 for the price of a Hamburger (H).
Now plug the value for H (2.25) into either equation.



The price for a Hamburger is $2.25
The price for a Hot Dog is $1.75