Tim has 2/3 as much money as Peter. After Tim received $120 from his mother and Peter used $120, Tim had twice as much money as Peter. How much money did Tim have at first?

Answer 1

Let X be the amount of money Peter has.
So, Tim has 2/3*X = (2*X)/3 as much money
After Tim received $120 from his mother, he has (2*X)/3 + 120 = 2*(X - 120) as much money.
Multiplying through the parentheses, we get (2*X)/3 + 120 = 2*X -240
Multiplying through by 3, we get 2*X + 360 = 6*X - 720
Subtracting 2*X and 360, we get 0 = 4*X - 1080
Adding 1080 to both sides, we get 1080 = 4*X
Dividing both sides by 4, we get X = 270
Then Tim had (2*270)/3 = $<<2*270/3=180>>180 at the start. Answer: \boxed{180}.