Question

lightbulbs act as resistors. janine is building a circuit that contains two lightbulbs in parallel. one of the lightbulbs has a resistance of 120 ohms, but the resistance of the second lightbulb is unknown. she models the total resistance in the circuit, t, with this equation, in which r represents the resistance of the second lightbulb.
$t = \frac{120r}{r + 120}$
find the inverse of janine’s equation.

Explanation:

Step1: Swap variables t and r

$$t = \frac{120r}{r + 120} \implies r = \frac{120t}{t + 120}$$

Step2: Cross-multiply to eliminate denominator

$$r(t + 120) = 120t$$

Step3: Distribute r on left side

$$rt + 120r = 120t$$

Step4: Isolate terms with r

$$rt - 120t = -120r$$
$$t(r - 120) = -120r$$

Step5: Solve for t

$$t = \frac{120r}{120 - r}$$

Answer:

$$t = \frac{120r}{120 - r}$$