Sarah is 4 years older than twice her brother. Together they are 34. How old is each?

Problem: Find the ages of Sarah and her brother, given that Sarah is 4 years older than twice her brother, and their combined age is 34.

Steps

1. Define variables
   $$\text{Let } b \text{ be the brother's age, and } 2b + 4 \text{ be Sarah's age.}$$
2. Set up the equation
   $$b + (2b + 4) = 34$$
3. Combine like terms
   $$3b + 4 = 34$$
4. Subtract 4 from both sides
   $$3b = 30$$
5. Divide both sides by 3
   $$b = 10$$
6. Calculate Sarah's age
   $$2(10) + 4 = 24$$