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

Explanation:

Answer 2

`M=(280)/(140) =2`

`C=2+5=7`

(2 Movies and 7 Commercials)

Explanation:

Let's represent every time Carson's songs are played in a commercial as C and in movies as M.

Set up the following equations:

`20C+120M=380` (1)

`C=M+5` (2)

Substitute equation 2 for equation 1:

`20(M+5)+120M=380`

Distribute:

`20M+100+120M=380`

Simplify:

`140M=280`

Divide both sides by 140:

`M=(280)/(140) =2`

Substitute 2 as M back into either original equation, I will use (2):

`C=2+5=7`