We are given a series circuit with two resistors and a voltage source. Since the resistor are in series this means that the total resistance is the sum of both resistances. Applying Ohm's law we get
[tex]V=I(R_1+R_2)[/tex]
Where:
V is voltage, I is current and R1 and R2 are the resistance of the radio and the variable resistance respectively.
Now we solve for the variable resistance, R2, first by dividing both sides by I:
[tex]\frac{V}{I}=R_1+R_2[/tex]
Now we subtract R1 to both sides:
[tex]\frac{V}{I}-R_1=R_2_{}[/tex]
Replacing the values:
[tex]\frac{15V}{0.2A}+60O\text{hm}=R_2[/tex]
Solving the operations:
[tex]\begin{gathered} 75Ohm+60Ohm=R_2 \\ 135Ohm=R_2 \end{gathered}[/tex]
Therefore, the resistance needed is 135 Ohms.