Answer
$$R= 30.0 \ \Omega .$$
Work Step by Step
We have
$$\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}$$
We plug in the $R$ values and find the common denominator ($150$) to combine the fractions:
$$\frac{1}{R}=\frac{1}{50}+\frac{1}{75}=\frac{3+2}{150}=\frac{5}{150}$$
Hence, we get
$$R=\frac{150}{5}=30.0 \ \Omega .$$
