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.

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