### Instruction: Uri buys two burgers and a soda for $\$2.10$, and Gen buys a burger and two sodas for $\$2.40$. How many cents does a soda cost?### Response: I need to find the price of a soda in cents, so I'll use some algebra to set up a system of equations based on the given information.
Let x be the price of a burger in cents, and y be the price of a soda in cents.
Then, Uri's purchase gives me the equation 2x + y = 210, and Gen's purchase gives me the equation x + 2y = 240.
I can use the elimination method to solve this system by multiplying the first equation by -2 and adding it to the second equation. This eliminates y and gives me -4x + x = -420 + 240, or -3x = -180.
Dividing both sides by -3, I get x = 60. So a burger costs 60 cents.
To find y, I can plug x = 60 into either equation. I'll use the first one: 2(60) + y = 210, or y = 210 - 120, or y = 90.
So a soda costs 90 cents.