Finding an unknown resistance in an Electric Circuit

[mlostrac]

Homework Statement

When connected in series to a 110-V line, two resistors use one-fourth the power
that is used when they are connected in parallel. If one resistor is
2.0 kΩ, what is the resistance of the other?

Homework Equations

1/Rt = 1/R1 +1/R2 (total resistance in parallel)
Rt = R1 + R2 (resistance in series)

Power = Current x Voltage

The Attempt at a Solution

So far my attempts have fizzled, ending with negative numbers.

Heres what I did:
1) Set the two hypothetical circuits (series and parallel) equal to each other by isolating the power:

P1 = 110^2/0.25(R1+R2)
P2 = 110^2(R1+R2)

And then isolating for R2 and solving (since we have R1 = 2000 ohms)

I ended up doing the quadratic equation and getting two negative numbers...

Any help would be appreciated :)

 

[kuruman]

P1 = 110^2/0.25(R1+R2)

Can you show why it this true?

P2 = 110^2(R1+R2)

The term R1+R2 must be in the denominator.

Anyway, I suggest that you work this symbolically. Find expressions

P_series = V²/R_eq,series
P_parallel = V²/R_eq,parallel
then take the ratio and say
P_series/P_parallel = 1/4.