Age Problem Calculator (Find Current Ages)

Solve the classic age word problem: from the age difference, a number of years later, and a multiple, find the current ages of parent and child.

Input

Enter the age difference, how many years later, and how many times the parent is the child to find their current ages.

Age difference (years)

Years later

Parent is x times child

Enter the difference as a positive whole number, the years as 0 or more, and the multiple as 2 or more.

Current ages

Child now

10 years

Parent now

38 years

How to solve

The difference never changes. If the child age is x, the parent is x + 28.

Write the condition that the parent is 3 times the child 4 years later.

Solving gives the child current age ( 28 minus 4 times ( 3 minus 1 ) ) / ( 3 minus 1 ) = 10 years.

The parent adds the difference back: 10 + 28 = 38 years.

Check

Child in 4 years

14 years

Parent in 4 years

42 years

42 divided by 14 = 3, so the condition holds.

The age difference stays the same as time passes. If the child current age is x and the difference is D, the parent current age is x + D.
After n years the child is x + n and the parent is x + D + n. The parent being m times the child gives ( x + D ) + n = m times ( x + n ).
Rearranging gives x = ( D minus n times ( m minus 1 ) ) / ( m minus 1 ), which is the child current age. The parent age adds the difference back.
If the child age is not a whole number that is 0 or more, the puzzle has no valid answer and the tool explains this.
Enter the multiple m as a whole number of 2 or more, the difference as a positive whole number, and the years as a whole number of 0 or more.

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