# Math Help - A puzzle

1. ## A puzzle

John was born in 19ab. The two digit number ab when divided by 2 gives his age on his birthday in 1999.

Can you tell me how old was he?

2. Originally Posted by getmath
John was born in 19ab. The two digit number ab when divided by 2 gives his age on his birthday in 1999.

Can you tell me how old was he?
1999 - age = 1900 + ab
age = ab/2

1999 - ab/2 = 1900 + ab
99 = 1.5 ab
ab = 66
age = 33

3. Hello, getmath!

Another approach . . .

John was born in $19ab$.
The two-digit number $ab$ when divided by 2 gives his age on his birthday in 1999.

Can you tell me how old was he?

Let $x\,=\,ab$

He was born in the year $1900 + x$

$\frac{x}{2}$ years later, it is 1999.

Hence: . $(1900 + x) + \frac{x}{2} \:=\:1999\quad\Rightarrow\quad x\:=\:66$

Therefore, he was born in $1966$; he was $33$ in 1999.

4. Originally Posted by TriKri
1999 - age = 1900 + ab
age = ab/2

1999 - ab/2 = 1900 + ab
99 = 1.5 ab
ab = 66
age = 33
Use of symbol "ab" here is not good because it can represent a*b.

You could've use x=ab as Soroban did.

Beside that, everything is ok.

I used formula
$1999 - \frac{{10a + b}}{2} = 1900 + 10a + b$
where $10a + b$ is that ab two digit number.

5. Originally Posted by OReilly
Use of symbol "ab" here is not good because it can represent a*b.

You could've use x=ab as Soroban did.

Beside that, everything is ok.

I used formula
$1999 - \frac{{10a + b}}{2} = 1900 + 10a + b$
where $10a + b$ is that ab two digit number.
Mathematically you are correct.