Old NCEES #529 (Electrical/Ctrl/Comm)

[OSPE]

I don't follow the NCEES solution to this problem, can anyone shed some light as to what values mean what? I can't seem to piece it together.

Q:

Consider the voltage waveform, x(t), which is the output of an amplitude-modulated (AM) transmitter:

x(t) = 40 cos (200,000pi t) + 10 cos (197,000pi t) + 10 cos (203,000pi t)

The percentage of modulation of the AM waveform, x(t), is most nearly:

( A ) 25

( B ) 33

( C ) 50

( D ) 75

A:

x(t) = 40 cos (200k pi t) + 10 cos (197k pi t) + 10 cos (203k pi t)

x(t) = 40 [cos (200k pi t) + 0.25 cos (197k pi t) + 0.25 cos (203k pi t)]

(Here's where I get lost - didn't see this in the EERM

max [1/2 m(t)] / A sub c = 0.25

max [ m(t)] = 20

Mod = 2 max [1/2 m(t)] / A sub c = 0.5 -> 0.5 * 100 = 50%

Any help would be appreciated. Trying to get some "last-minute" concepts down before Friday.