jmc

Let's work with this problem in cents, not dollars, because the answer calls for a number in cents. So, Alice's three burgers and two sodas cost 320 cents and Bill's food costs 200 cents. Let a burger cost $b$ cents and a soda cost $s$ cents. We are trying to find the value of $b$. We can set up a system of two equations to represent the given information. These equations are:

$$\begin{array}{rl}3b+2s& =320\\ 2b+s& =200\end{array}$$We are solving for $b$, so we want to eliminate $s$ from the equations above. Multiplying both sides of the second equation by 2, we get $4b+2s=400$, or $2s=400-4b$. Substituting this equation into the first equation above to eliminate $s$, we get that $3b+(400-4b)=320$, or $b=80$. Thus, a burger costs $\boxed{80}$ cents.