If I give my brother $5$ dollars, then we will have the same amount of money. If instead he gives me $10$ dollars, then I'll have twice as much money as he will have. How much money does my brother currently have (in dollars)?
Lets say that the amount I currently have is x, and the amount my brother has is y.
We can set up the following equations:
\(x-5 = y+5\)
\(2(y-10) = x+10\)
Simplifying the system of equations, we get:
\(x=y+10 \\ 2y - 30 = x\)
Now, we can solve for y:
\(y+10=2y-30\\ -y=-40\\ y=40\)
Therefore, my brother currently has $40.