3 Made the answer not spoiler-only; Mathjaxed the explanation
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Charles was born in

Charles was born in 1976 and in 1999 he is 23$1976$

so in 1999 he is

$23$ years old.

His

Explanation:

His date of birth is 19xy$19xy$ and we know that his age in 1999 $1999$ (which is 99 - (10x + y)$99 - (10x + y)$) is equal to the sum of digits 1 + 9 + x + y.

99 - 10x$1 + 9 + x + y$.

This gives us:

- y = 1 + 9 + x + y$99 - 10x - y = 1 + 9 + x + y$
11x + 2y = 89$11x + 2y = 89$
x$x$ and y$y$ must be between 0$0$ and 9$9$

We are left with 4 possibilities:

For $0 \le x \le 6 \rightarrow y > 9$
for x between 0 and 6, y would be over 10For $x = 7 \rightarrow y = 6$
for x = 7, y = 6,For $x = 8 \rightarrow y = 0.5$
for x = 8, y = 0.5, which is not an integerFor $x = 9 \rightarrow y = -0.5$

The only feasible solution is:

$x = 7,\ y = 6$
for x = 9, y =Since -5, which is not$y$ has to be a positive integer., but cannot be greater than 9

Charles was born in 1976 and in 1999 he is 23 years old.

His date of birth is 19xy and we know that his age in 1999 (which is 99 - (10x + y)) is equal to the sum of digits 1 + 9 + x + y.

99 - 10x - y = 1 + 9 + x + y
11x + 2y = 89
x and y must be between 0 and 9
for x between 0 and 6, y would be over 10
for x = 7, y = 6,
for x = 8, y = 0.5, which is not an integer
for x = 9, y = -5, which is not a positive integer.

Charles was born in

$1976$

so in 1999 he is

$23$ years old.

Explanation:

His date of birth is $19xy$ and we know that his age in $1999$ (which is $99 - (10x + y)$) is equal to the sum of digits $1 + 9 + x + y$.

This gives us:

$99 - 10x - y = 1 + 9 + x + y$
$11x + 2y = 89$
$x$ and $y$ must be between $0$ and $9$

We are left with 4 possibilities:

For $0 \le x \le 6 \rightarrow y > 9$
For $x = 7 \rightarrow y = 6$
For $x = 8 \rightarrow y = 0.5$
For $x = 9 \rightarrow y = -0.5$

The only feasible solution is:

$x = 7,\ y = 6$
Since $y$ has to be a positive integer, but cannot be greater than 9

2 added 315 characters in body
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Charles was born in 1976 and in 1999 he is 23 years old.

His date of birth is 19xy and we know that his age in 1999 (which is 99 - (10x + y)) is equal to the sum of digits 1 + 9 + x + y.

99 - 10x - y = 1 + 9 + x + y
11x + 2y = 89
x and y must be between 0 and 9
for x between 0 and 6, y would be over 10
for x = 7, y = 6,
for x = 8, y = 0.5, which is not an integer
for x = 9, y = -5, which is not a positive integer.

Charles was born in 1976 and in 1999 he is 23 years old.

Charles was born in 1976 and in 1999 he is 23 years old.

His date of birth is 19xy and we know that his age in 1999 (which is 99 - (10x + y)) is equal to the sum of digits 1 + 9 + x + y.

99 - 10x - y = 1 + 9 + x + y
11x + 2y = 89
x and y must be between 0 and 9
for x between 0 and 6, y would be over 10
for x = 7, y = 6,
for x = 8, y = 0.5, which is not an integer
for x = 9, y = -5, which is not a positive integer.

1
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Charles was born in 1976 and in 1999 he is 23 years old.