Age problems
Relate two ages now and at another time, then solve for one of them.
The shape of an age question
You are told how two people’s ages relate now, and asked about their ages at another time.
Maya is 3 times as old as Sam. In 4 years she will be twice his age. How old is Sam now?
Use a letter for the younger person
Let Sam = s. Then Maya = 3s.
In 4 years: Sam is s + 4, Maya is 3s + 4.
The question says Maya will then be twice Sam: 3s + 4 = 2(s + 4)
Expand: 3s + 4 = 2s + 8, so s = 4. Sam is 4, Maya is 12. Check: in 4 years, 8 and 16. Twice. ✓
The rule that catches people out
Both people age by the same amount. If four years pass, you add 4 to both. It sounds obvious, and it is the single most common slip in these questions.
How to attack this question type
- 1
Always let the letter stand for the YOUNGER person. It keeps the numbers whole and the algebra simpler.
- 2
Add the same number of years to everyone. This is the mistake to guard against above all others.
- 3
Write the "in N years" expressions before writing the equation. Rushing straight to an equation is where sign errors come from.
- 4
Always check your answer back against the original wording. It takes five seconds and catches nearly every slip.
Practice · untimed
Maya is 3 times as old as Sam. In 4 years she will be twice his age. How old is Sam now?
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