Math Made Simple
Solving Age Word Problems with Algebra: A Step-by-Step Approach
Learn how to turn age clues into equations and solve family, sibling, and future-age problems with confidence.
The big idea
Age problems are algebra problems because an unknown age can be represented by a variable. The most important fact is that an age difference stays the same over time. If one person is 6 years older today, that person will still be 6 years older in 5 years.
The age-problem formula
This shortcut works when you know the sum of two ages and the constant difference between them. The older age is the younger age plus the difference.
On a small phone screen, swipe horizontally inside the formula box if the equation feels wide.
The five-step approach
- Choose the reference time. Decide whether the problem describes ages now, in the future, or in the past.
- Define one age. Let x represent the younger person’s age unless another choice is simpler.
- Express the other age. Use x + difference for an older person or x − difference for a younger person.
- Write and solve the equation. Translate words such as “sum,” “times,” and “in 5 years.”
- Check the story. Substitute both ages back into the original conditions and include the correct time frame.
Time-shift rules
When time changes, add or subtract the same number of years from every person:
For example, if a child is x years old now, the child will be x + 6 in 6 years and x − 6 six years ago. The difference between two people does not change when the same time is added or subtracted from both ages.
On a small phone screen, swipe horizontally inside the rule box if needed.
Worked examples
Example 1: Sibling ages with a known sum
Story: Two siblings are 6 years apart. Their ages add up to 34. How old are they?
Define: Let the younger sibling be x. The older sibling is x + 6.
Answer: The siblings are 14 and 20 years old. Check: 14 + 20 = 34 and 20 − 14 = 6.
Example 2: A parent’s age is a multiple
Story: A parent is 3 times as old as a child. Their ages add up to 56. Find both ages.
Define: Let the child’s age be x. The parent’s age is 3x.
Answer: The child is 14 years old and the parent is 42 years old. Check: 14 + 42 = 56 and 42 = 3 × 14.
Example 3: Ages in the future
Story: Ana is 4 years older than Ben. In 6 years, their ages will add up to 40. How old are they now?
Define: Let Ben’s current age be x. Ana’s current age is x + 4. In 6 years, the ages are x + 6 and x + 10.
Answer: Ben is 12 now and Ana is 16 now. In 6 years they will be 18 and 22, and 18 + 22 = 40.
Example 4: A ratio with a future total
Story: An aunt is 4 times as old as her niece now. In 6 years, their ages will add up to 72. Find their current ages.
Define: Let the niece’s current age be x. The aunt’s current age is 4x. In 6 years, the ages are x + 6 and 4x + 6.
Answer: The niece is 12 now and the aunt is 48 now. In 6 years they will be 18 and 54, and 18 + 54 = 72.
A quick reference table
| Phrase | Algebra translation | Meaning |
|---|---|---|
| 6 years older than x | x + 6 | Add 6 years |
| 6 years younger than x | x − 6 | Subtract 6 years |
| 3 times x | 3x | Multiply by 3 |
| sum of two ages is 40 | first + second = 40 | Add both ages |
On a small phone screen, swipe horizontally inside the table to view every column.
Memory tip
“Pick now, shift together, check twice.” Pick one current age as x, shift every age by the same number of years, and check both the total and the relationship. If the difference or ratio is part of the story, verify that clue too.
Common mistakes to avoid
- Do not add the time shift to only one person. In 6 years, every person is 6 years older.
- Do not confuse “3 times as old” with “3 years older.” The first means 3x; the second means x + 3.
- Be careful with “younger than.” “6 years younger than x” means x − 6.
- Do not forget whether the question asks for current ages or ages in the past or future.
- Reject an impossible result, such as a negative age. Recheck the equation and the wording.
Practice questions
Define a variable, write an equation, solve it, and check the original age conditions.
- Two siblings are 8 years apart and their ages add up to 42. Find both ages.
- A parent is 4 times as old as a child. Their ages add up to 60. Find both ages.
- One friend is 2 years older than another. In 4 years, their ages will add up to 50. Find their current ages.
- A grandfather is 5 times as old as a grandchild. Their current ages add up to 72. Find both ages.
- In 5 years, a teenager will be 20 years old. How old is the teenager now?
Answers
- 17 and 25. Let the younger age be x: x + (x + 8) = 42, so 2x = 34 and x = 17.
- 12 and 48. Let the child’s age be x: x + 4x = 60, so 5x = 60 and x = 12.
- 20 and 22. Let the younger age be x: (x + 4) + (x + 2 + 4) = 50, so 2x + 10 = 50 and x = 20.
- 12 and 60. Let the grandchild’s age be x: x + 5x = 72, so 6x = 72 and x = 12.
- 15 years old. If the current age is x, then x + 5 = 20, so x = 15.
Final takeaway
Age word problems become much easier when you anchor the problem in one variable. Write every age in terms of that variable, shift all ages equally when time changes, solve the equation, and check the result against the story.
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