Question

Ariana is a songwriter who collects royalties on her songs

whenever they are played in a commercial or a movie. She
will earn $30 every time one of her songs is played in a
commercial and she will earn $110 every time one of her
songs is played in a movie. Ariana earned a total of $620
in royalties dn 10 commercials and movies. Write and
solve a system of equations to determine the number of
commercials and the number of movies on which her songs
were played.

number of commercials:
number of movies:

Answer 1

number of commercials: 6

Number of movies: 4

Explanation:

Let x = the number of commercials

Let y = the number of movies

30x + 110 y = 620

x + y = 10 This can be written y = 10 - x (substitute 10 - x for y)

30x + 110y = 620

30x + 110(10 - x) = 620 Distribute the 110

30x + 1100 - 110x = 620 Combine like terms

-80x + 1100 = 620 Subtract 1100 from both sides

-80x = -480 Divide both sides by -80

x = 6

There are 6 commercials.

Substitute 6 for x

x + y = 10

6 + y = 10 Subtract 6 from both sides

y = 4

There are 4 movies.

Check:

x + y = 10

6 + 4 = 10

10 = 10 checks

30x + 110y = 620

30(6) + 110(4) = 620

180 + 440 = 620

620 = 620 checks