Your question is great.
This is how you solve it.
The original price of the cake is 100% of the price of the cake.
She got a 40% discount on the cake.
100% - 40% = 60%
That means she paid only 60% of the price of the cake.
She paid $420.
60% of what number is 420?
60% of x = 420
60% * x = 420
0.6x = 420
Divide both sides by 0.6:
x = 700
Answer: The original price of the cake was $700.
BTW, if you continue writing numbers in your solution, you will get to 700 above 100%. That would be the correct solution, so you're on the right track.
P.S.
Can you please let me know which bakery makes a $700 cake? I'd like to taste it.