What resistance must be placed in parallel with a 149 Ohm resistor to make the equivalent resistance 124 Ohm?
Well, we use the formula for parallel resistors to find the equivalent resistance for two resistors:
$\displaystyle \text{We have the following information: }$
$\displaystyle R_1 = 149 \Omega$
$\displaystyle R_{Total} = 124 \Omega$
$\displaystyle \text{The Equation is: }$
$\displaystyle \frac{1}{R_{Total}} = \frac{1}{R_1} + \frac{1}{R_2}$
$\displaystyle \frac{1}{124} = \frac{1}{149} + \frac{1}{R_2}$
$\displaystyle \frac{1}{124} - \frac{1}{149} = \frac{1}{R_2}$
$\displaystyle \frac{149}{18476} - \frac{124}{18476} = \frac{1}{R_2}$
$\displaystyle \frac{25}{18476} = \frac{1}{R_2}$
$\displaystyle R_2*\frac{25}{18476} = 1$
$\displaystyle 25R_2 = 18476$
$\displaystyle R_2 = \frac{18476}{25}$
$\displaystyle R_2 = 739.04 \Omega$
And there you go.