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

• 7 commercials
• 2 movies

Explanation:

You want to know the number of commercials and movies playing Carson's song if his $380 in royalties include $20 for each commercial play and $120 for each movie play. There were 5 more commercial plays than movie plays.

Equations

We can describe the numbers of commercial (c) and movie (m) plays by ...

20c +120m = 380

c - m = 5

Solution

Using c = m +5, we can substitute for c to get ...

20(m +5) +120m = 380

140m +100 = 380 . . . . . . . simplify

140m = 280 . . . . . . . . . . subtract 100

m = 2 . . . . . . . . . . . . . . divide by 140

c = 2 +5 = 7

Carson's songs were played on 7 commercials and 2 movies.

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