CE Board Exam Randomizer

Age Problems

Age problems involve translating relationships about people’s ages — either in the present, past, or future — into algebraic expressions or equations.

Common Phrases in Age Problems:

• "x years ago" → Subtract: $x - \text{years}$
• "in x years" → Add: $x + \text{years}$
• "Twice as old" → Multiply: $2x$
• "Half as old" → Divide: $\frac{x}{2}$
• "The difference in age" → Subtract one from the other

Typical Structure:

Let one person’s age be a variable (e.g., $x$), and express the others in terms of $x$.

Problem 1:

Itadori is 4 years younger than Megumi. Twenty years ago, Megumi’s age was 13 years more than half the age of Itadori. How old are they now? Ans. Megumi = 42, Itadori=38

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Problem 2:

When I am as old as my father is now, I shall be five times as old as my son is now. By then, my son will be eight years older than I am now. The combined ages of my father and me is 100 years. How old is my son? Ans. 13

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Problem 3:

Six years ago, Tom was five times as old as Ana. In five years, Tom will be three times as old as Ana. What is the present age of Ana? Ans. 17

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