Light bulbs in Series

Romperstomper
A 60W-120V bulb and a 200W-120V bulb are connected in a series across a 240V line. Assume that the resistance of each bulb does not vary with current.(Note:The 60W-120V means it dissipates 60W when connected to a 120V line, and the 200W-120V means it dissipates 200W when connected to a 120V line). Find the current running through the bulbs.

What I did: The voltage is double, so I figured that if the voltage is doubled, the power must be doubled since $$P = I * \Delta V$$ and the current remains the same. Since $$\Delta V$$ changes between each bulb, I decided to use the net power and solved for I.

$$520 = I * 240 = 2.17A$$. This is way off from the answer of .769A. Can anyone tell me what I did wrong?