Tim has 2/3 as much money as Peter. After Tim received $120 from his mother and Peter used $120...

[ronnieyoe225]

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?

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.

 

[Steven G]

You need to define YOUR variables. It is must so YOU understand YOUR equations.

I suspect that X represents the money that Peter has.

Now solve your equation: (2*X)/3 + 120 = 2*(X - 120)

Is there a reason that you didn't continue? Can you please explain what the trouble is?
Hint: First distribute the 2 and then multiply both sides by 3

 

[khansaheb]

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?

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.

If I were to solve this problem, I would start:

Assume

the amount of that Tim has, now, is X (I would have preferred to call it T)

the amount of that Peter has, now, is Y (I would have preferred to call it P)

Given:

Tim has 2/3 as much money as Peter → X = 2/3 * Y .....................................eqn (1)

After Tim received $120 from his mother and Peter used $120, Tim had twice as much money as Peter→ X +120 = 2*(Y-120) ................ (2)

X +120 = 2*Y - 240

X = 2 * Y - 360 ..........................Now use (1) here

2/3 * Y = 2*Y - 360

(1+1/3) * Y = 360

Y = 360 / (4/3) =270

Now use this value of Y in (1) to calculate X.

Finally, check your answer, by using calculated values of X & Y in (2).