Study guides › Level 6 · Master

Age puzzles

Level 6 · Master · for questions like “In 6 years, Diego will be twice as old as Diego was 3 years ago. How old is Diego now?”

💡 The idea

Call the age now x. Write every other age using x, then make the sentence into an equation.

🪜 The steps

1. Now: x. In 6 years: x + 6. 3 years ago: x − 3.
2. Turn “twice as old as” into an equation: x + 6 = 2(x − 3).
3. Solve it.

✏️ Worked examples

1. x + 6 = 2(x − 3). Multiply out: x + 6 = 2x − 6. So x = 12.

Check: in 6 years Diego is 18, and 3 years ago Diego was 9. 18 is twice 9. ✓

2. In 4 years, Maya will be three times as old as 4 years ago. x + 4 = 3(x − 4), so x + 4 = 3x − 12, 2x = 16 and x = 8.

⚠️ Watch out

• Multiply out the bracket fully: 2(x − 3) = 2x − 6, not 2x − 3.
• Always check by putting your answer back into the story.

🎯 Try these

1. In 5 years, Sam will be twice as old as 5 years ago.
2. In 10 years, Ana will be twice as old as 2 years ago.
3. In 2 years, Leo will be three times as old as 6 years ago.

Answers: 1) 15 2) 14 3) 10

This guide is also in the 10MathQ app: tap “📖 Study guide” after a question.