Age Word Problem Calculator – Three People
Find three ages from their sum and the two consecutive age differences.
Formula
Youngest = (sum − 2g₁ − g₂)/3; middle = youngest + g₁; oldest = middle + g₂
Youngest age (years) ≈ max(0,(10)) · Middle age (years) ≈ (10)+(5) · Oldest age (years) ≈ (15)+(10)
How to use
- Enter the sum of the three ages in years.
- Enter middle minus youngest, then oldest minus middle.
- Read the ages and check their sum.
Examples
- Total 50, gaps 5 and 10 give ages 10, 15 and 25 years.
Frequently asked questions
Which gap goes first?
g₁ is the middle age minus the youngest; g₂ is the oldest minus the middle. Both are nonnegative.
Can the ages be fractional?
Yes. This solves a linear word problem in years, not completed birthdays from dates.
What if the data imply a negative age?
That input is rejected. The total must be at least 2g₁ + g₂; tiny floating-point errors at zero are treated as zero.
Sources
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