To solve for the value of R, its voltage and current should be determine.
To do so, consider the two loads, R and L1.
Since they are in series, the current passing through L1 and R are the same.
So, use the voltage rating and power consumption of L1 to get `I_R` .
then the current of R is:
Furthermore, when the loads are in series, the sum of the voltage across each load is equal to voltage supply.
So the voltage across R is,
Now that I_R and V_R are known, apply the formula of Ohm's Law to get its resistance.
Hence, the resistance of R is 36 ohms.