jmc

Let's work with this problem in cents, not dollars, because the answer calls for a number in cents. So, Uri's two burgers and a soda cost 210 cents and Gen's food costs 240 cents. Let a burger cost $b$ cents and a soda cost $s$ cents. We are trying to find the value of $s$. We can set up a system of two equations to represent the given information. These equations are:

$$\begin{array}{rl}2b+s& =210\\ b+2s& =240\end{array}$$

We are solving for $s$, so we want to eliminate $b$ from the equations above. Multiplying both sides of the second equation by 2, we get $2b+4s=480$, or $2b=480-4s$. Substituting this equation into the first equation above to eliminate $b$, we get that $(480-4s)+s=210$, or $s=90$. Thus, a soda costs $\boxed{90}$ cents.