Answer
$R = 900~\Omega$
Work Step by Step
We can find the value of $R$:
$V_{out} = \frac{V_{in}~R_2}{R_1+R_2}$
$V_{out} = \frac{V_{in}~100~\Omega}{R+100~\Omega}$
$\frac{V_{in}}{10} = \frac{V_{in}~100~\Omega}{R+100~\Omega}$
$R+100~\Omega = (10)(100~\Omega)$
$R = 900~\Omega$
