If I give my brother 5 dolalrs, then we will have the same amount of money. If instead he gives me 14 dollars, then I'll have twice as much money as he will have. How much money does my brother currently have (in dollars)?
Let's set up some variables here. Let x be your money, and b be your brother's money.
If you give your brother five dollars, the equation will be x - 5 = b + 5.
However, if your brother gives you 14 dollars, you can set up the equation x + 14 = 2(b-14) because you have twice as much as him.
Now we have the system of equations:
x - 5 = b + 5
x + 14 = 2(b - 14) = 2b-28 ==> x + 14 = 2b - 28
Using substitution in the first equation, x = b + 10. Now we can solve for b:
b + 10 + 14 = 2b - 28 ==> b + 24 = 2b - 28
Subtract b on both sides and add 28 and get:
52 = b. Therefore, your brother has 52 dollars.