# Archive — hermiene.net

"Holding a key, you may infer the existence of a lock. However, do not make the mistake of assuming that yours is the only key."

### April 30, 2003

I was extremely fascinated by a small, but very cozy math problem today. Many thanks to Even for helping me figure it out. A little tweaked, the problem goes as follows:

Three guys, Alex, John and Jacob, have their own hard drives. The sum of all their space is $230 GB$. Alex has $10 GB$ more than John, and Jacob has twice as much as Alex. What did each of them have?

We want someone to have $x$ gigabytes. The obvious choice is John, since both Alex and Jacob refer to him. So:

Alex: $x + 10$
John: $x$
Jacob: $2(x + 10)$

Next, we sum them up, and equal them to $230$:

$x + 10 + x + 2(x + 10) = 230$
$x + 10 + x + 2x + 20 = 230$

We rearrange them...

$4 x = 230 - 20 - 10$
$4x = 200$
$x = 50$

There you go. John has $50$ gigabytes of sweet hard drive space. Unless you are completely incompetent, you should be able to figure out how much space Alex and Jacob had.