In 1998, Cathy's age is equal to the sum of the four digits in the year of her birthday, then how old was Cathy in 1998?

Cathy was born in 1980 and she was 18 years old in 1998

Step-by-step explanation:

Equations

This is a special type of equations where all the unknowns must be integers and limited to a range [0,9] because they are the digits of a number.

Let's say Cathy was born in the year x formed by the ordered digits abcd. A number expressed by its digits can be calculated as

In 1998, Cathy's age was

And it must be equal to the sum of the four digits

Rearranging

We are sure a=1, b=9 because Cathy's age is limited to having been born in the same century and millennium. Thus

Operating

If now we try some values for c we notice there is only one possible valid combination, since c and d must be integers in the range [0,9]

c=8, d=0

Thus, Cathy was born in 1980 and she was 18 years old in 1998. Note that 1+9+8+0=18

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