If I give my brother 5 dollars, then we will have the same amount of money. If instead he gives me 12 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 call the amount of money my brother currently has "x".
From the first statement, we know that after I give him 5 dollars, we will have the same amount of money, so x + 5 = x.
From the second statement, we know that after he gives me 12 dollars, I will have twice as much money as he will, so x + 12 = 2x.
Solving for x:
x + 5 = x x = 5
x + 12 = 2x 5 + 12 = 2x 17 = 2x x = 8.5
So my brother currently has 8.50 dollars.
Y - 5 ==B + 5,
Y + 12==2[B - 12], solve for B, Y
Use substitution to get:
B==$46.00 - what your brother started with
Y ==$56.00 - what you started with
56 - 5 == 46 + 5 - when you gave your brother $5, then you both had:
$51 == $51
56 + 12 ==46 - 12 - when your brother gave you $12, then you had:
$68 ==$34 - you will have twice as much as your brother.