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Hailey is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Hailey will earn $ 30 $30 every time one of her songs is played in a commercial and she will earn $ 100 $100 every time one of her songs is played in a movie. Hailey’s songs were played on 4 times as many commercials as movies and her total earnings on the royalties from all commercials and movies was $440. Determine the number of commercials and the number of movies on which Hailey’s songs were played.
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Let’s use the variables c c and m m to represent the number of times Hailey’s songs were played in commercials and movies, respectively.
We know that Hailey earns $ 30 $30 every time one of her songs is played in a commercial, so her total earnings from commercials would be 30 c 30 c. Similarly, her total earnings from movies would be 100 m 100 m.
We are told that Hailey’s songs were played on 4 times as many commercials as movies, so we can write:
c = 4 m c=4m
We are also told that Hailey’s total earnings on the royalties from all commercials and movies was $ 440 $440, so we can write:
30 c + 100 m = 440 30 c+100 m=440
Now we can substitute c = 4 m c=4m into the second equation and solve for m m:
30 c + 100 m = 440 30 ( 4 m ) + 100 m = 440 220 m = 440 m = 2 {:[30 c+100 m=440],[],[30(4m)+100 m=440],[],[220 m=440],[],[m=2]:}
So Hailey’s songs were played in 2 movies.
To find the number of commercials, we can use c = 4 m c=4m:
c = 4 ( 2 ) = 8 c=4(2)=8
So Hailey’s songs were played in 8 commercials.
Therefore, Hailey’s songs were played in 8 commercials and 2 movies.
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