Carter is a songwriter who collects royalties on his songs whenever they are played in a commercial or a movie. Carter will earn $50 every time one of his songs is played in a commercial and he will earn $130 every time one of his songs is played in a movie. Carter earned a total of $1000 in royalties on 12 commercials and movies. Determine the number of commercials and the number of movies on which Carter's songs were played.

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absor201 absor201 · Answer 1 · 2019-12-09T18:48:34+01:00

Carter's song played on 7 commercials and 5 movies.

Step-by-step explanation:

Earning per commercial = $50

Earning per movie = $130

Total earned = $1000

Total commercial and movies = 12

Let,

x be the number of commercials

y be the number of movies

According to given statement;

x+y=12 Eqn 1

50x+130y=1000 Eqn 2

From Eqn 1

x=12-y Eqn 3

Putting value of x from Eqn 3 in Eqn 2

[tex]50(12-y)+130y=1000\\600-50y+130y=1000\\80y=1000-600\\80y=400[/tex]

Dividing both sides by 80

[tex]\frac{80y}{80}=\frac{400}{80}\\y=5[/tex]

Putting y=5 in Eqn 1

[tex]x+5=12\\x=12-5\\x=7[/tex]

Carter's song played on 7 commercials and 5 movies.

Keywords: linear equation, substitution method

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