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?
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. 