2021 AMC 12A Problem 6

A deck of cards has only red cards and black cards. The probability of a randomly chosen card being red is \frac13. When 4 black cards are added to the deck, the probability of choosing red becomes \frac14. How many cards were in the deck originally?

\textbf{(A) }6 \qquad \textbf{(B) }9 \qquad \textbf{(C) }12 \qquad \textbf{(D) }15 \qquad \textbf{(E) }18

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.