Answer
The larger value of the filament resistance is $~~144~\Omega$
Work Step by Step
We can write an expression for the power:
$P = \frac{V^2}{R}$
At $100~W$, the current passes through the filament with the larger resistance
At $200~W$, the current passes through the filament with the smaller resistance
At $300~W$, the current passes through the filaments wired in parallel
We can find the larger value of the filament resistance:
$P = \frac{V^2}{R}$
$R = \frac{V^2}{P}$
$R = \frac{(120~V)^2}{100~W}$
$R = 144~\Omega$
The larger value of the filament resistance is $~~144~\Omega$
