If you give me $100, then I will have half as much money as you, but if I give you $100, then you'll have five times as much money as I do. How much does each of us have now?

This clever brain teaser is a classic example of a "word problem" that can be elegantly solved using algebra. To figure out how much money each person has, we assign variables to the unknown amounts. Let's say 'I' represents my current money and 'Y' represents your current money. The trick is to translate each part of the scenario into a mathematical equation, then solve those equations simultaneously.

The first condition states: "If you give me $100, then I will have half as much money as you." This means my new amount (I + $100) would be half of your new amount (Y - $100). This gives us the equation: I + 100 = (Y - 100) / 2. The second condition says: "If I give you $100, then you'll have five times as much money as I do." Here, your new amount (Y + $100) would be five times my new amount (I - $100). This translates to: Y + 100 = 5(I - 100).

Now we have a system of two linear equations