The scribbles around the pic was just me trying to make sense of the conflicting info.
It isn't conflicting, and your assumption that the light bulbs are supplied with 120 volts is incorrect, but irrelevant. Using the equation that P x R = V
^{2}, and substituting the values indicated for power and resistance, yields a value for V (after extracting the square root of the product of power and resistance) that is close to 110 volts instead of the 120 volts you used to calculate the current in each lamp. In any event, it is assumed that the
voltage applied to household lamps is constant, so using the relationship that P = V
^{2} / R it is easily seen that reducing the value of R will have the effect of increasing the value of P.
All of the relationships between V, I, R, and P for a particular circuit are algebraic derivatives of equations expressing Ohm's Law (V = I x R) and power (P = V x I), as
@Harald Kapp mentioned in post #3 and
@bertus illustrated in post #4. You just need to be careful when, where, and how you apply those equations.
Learn about Kirchoff's voltage law (algebraic sum of voltage around a loop is always zero) and current law (algebraic sum of currents into and out of a circuit node is always zero). These two laws, along with Ohm's Law, will allow you to analyze more complicated situations, such as circuits involving bridged resistances and two or more voltage and/or current sources. You should also be familiar with how to solve simultaneous equations and the superposition theorem, both of which are useful for analyzing circuits.