Carson is a songwriter who collects royalties on his songs whenever they are played in a commercial or a movie. Carson will earn $20 every time one of his songs is played in a commercial and he will earn $120 every time one of his songs is played in a movie. Carson's songs were played on 5 more commercials than movies, and his total earnings on the royalties from all commercials and movies was $380. Determine the number of commercials and the number of movies on which Carson's songs were played.

Question

Carson is a songwriter who collects royalties on his songs whenever they are played in a commercial or a movie. Carson will earn $20 every time one of his songs is played in a commercial and he will earn $120 every time one of his songs is played in a movie. Carson's songs were played on 5 more commercials than movies, and his total earnings on the royalties from all commercials and movies was $380. Determine the number of commercials and the number of movies on which Carson's songs were played.

Answer 1

Let:

x = number of times Carson's songs were played in a movie
x + 5 = number of times Carson's songs were played in a commercial

The total earnings from movies is $120x
The total earnings from commercials is $20(x + 5)

Given that the total earnings from all commercials and movies was $380, we can write the following equation:
120x + 20(x + 5) = 380
120x + 20x + 100 = 380
140x = 280
x = 2

Therefore, Carson's songs were played in 2 movies and 7 commercials.