The sum of two numbers is 45 and their difference is 11. What is the larger number?

Explanation

1. 01

   Call the numbers $x$ and $y$, with $x$ the larger, so $x + y = 45$ and $x - y = 11$.

2. 02

   Adding the two equations eliminates $y$: $2x = 56$, so $x = 28$.

3. 03

   Then $y = 45 - 28 = 17$.

4. 04

   Check: $28 + 17 = 45$ and $28 - 17 = 11$.