1. **State the problem:** Shane is twice as old as Annie. Ten years ago, Shane's age was thrice Annie's age. We need to find their present ages. 2. **Define variables:** Let Annie's present age be $x$ years. 3. **Express Shane's age:** Since Shane is twice as old as Annie, Shane's present age is $2x$ years. 4. **Form the equation from the condition 10 years ago:** Ten years ago, Shane's age was $2x - 10$ and Annie's age was $x - 10$. According to the problem, Shane's age then was thrice Annie's age: $$2x - 10 = 3(x - 10)$$ 5. **Solve the equation:** $$2x - 10 = 3x - 30$$ Subtract $2x$ from both sides: $$-10 = x - 30$$ Add 30 to both sides: $$20 = x$$ 6. **Find Shane's age:** $$2x = 2 \times 20 = 40$$ 7. **Answer:** Annie is 20 years old and Shane is 40 years old now.