Question

Owen is a songwriter who collects royalties on his songs whenever they are played in a commercial or a movie. Owen will earn $50 every time one of his songs is played in a commercial and he will earn $140 every time one of his songs is played in a movie. Owen's songs were played on 4 more commercials than movies, and his total earnings on the royalties from all commercials and movies was $770. Determine the number of commercials and the number of movies on which Owen's songs were played.

Answer 1

Owen's songs were played on 3 movies and on 7 commercials.

Explanation:

System of Equations

Let's call C the number of commercials on which Owen's songs were played and M the number of movies on which Owen's songs were played. We know Owen's songs were played on 4 more commercials than movies, it can be expressed as

`C=M+4`

Owen will earn $50 every time one of his songs is played in a commercial and he will earn $140 every time one of his songs is played in a movie, so his total earnings are

`140M+50C=770`

We have a system of linear equations that can be easily solved by using the formula for C in the above equation

`140M+50(M+4)=770`

Operating

`140M+50M+200=770`

Reducing

`190M=770-200=570`

Solving

`M=570/190=3`

The number of commercials is

`C=M+4=7`

Owen's songs were played on 3 movies and on 7 commercials.