### Instruction: Alice buys three burgers and two sodas for $\$3.20$, and Bill buys two burgers and a soda for $\$2.00$. How many cents does a burger cost?### Response: Let's call the price of a burger x.
And let's call the price of a soda y.
Now we can set up the equations: 3x+2y=320 and 2x+y=200.
We could solve this system either by substitution or elimination method.
I like elimination. Let's multiply the second equation by 2 so we can eliminate y.
So now the equations are: 3x+2y=320 and 4x+2y=400.
Let's subtract the first equation from the second one.
That gives us x=80.
So a burger costs 80 cents.
To check our answer, let's substitute x in one of the equations.
Let's use the second one. So 2x+y=200 -> 2*80+y=200.
That simplifies to 160+y=200.
So y=40.
So a soda costs 40 cents.