The sum of two numbers is $30$. Their difference is $4$. What is the larger of the two numbers?
I need to find two numbers that add up to 30 and have a difference of 4. Let me try to write this as a system of equations: x + y = 30 and x - y = 4. I can solve this system by adding the two equations together. That would eliminate y and give me 2x = 34. Dividing both sides by 2, I get x = 17. That means y = 30 - 17 = 13. So the two numbers are 17 and 13, and the larger one is 17. 