I see what u did there. Im used to doing source voltage/ desired current= resistanceto use. Calculating from his schematic I took the led forward voltage divided by 20mA to get a rough led resistance, added those resistance values together to get a rough led total resistance, subtracted that from the 470 ohm value and ended with about the same resistors used.Resistor for LED==(Supply Voltage - LED Vforward)/20 mA
Example:
(9 V - 2.71 V - 3.73 V)/20 mA= 128 Ohm (he rounded down to 120 Ohm)
Power for resistor == I*I*R == 20 mA*20 mA*120 Ohm=0.048 W (he round it up to 1/8 W which is 0.125 W for extra safety margin)