Owen is a songwriter who collects royalties on his songs whenever they are played in a commercial or a movie. Owen will earn $50 every time one of his songs is played in a commercial and he will earn $140 every time one of his songs is played in a movie. Owen's songs were played on 4 more commercials than movies, and his total earnings on the royalties from all commercials and movies was $770. Determine the number of commercials and the number of movies on which Owen's songs were played.
Answers
Answer:
Owen will earn $50 every time one of his songs is played in a commercial and he will earn $140 every time one of his songs is played in a movie. Owen's songs were played on 4 more commercials than movies, and his total earnings on the royalties from all commercials and movies was $770.
Answer:
Owen's songs were played on 3 movies and on 7 commercials.
Step-by-step explanation:
System of Equations
Let's call C the number of commercials on which Owen's songs were played and M the number of movies on which Owen's songs were played. We know Owen's songs were played on 4 more commercials than movies, it can be expressed as
C=M+4C=M+4
Owen will earn 50 every time one of his songs is played in a commercial and he will earn50everytimeoneofhissongsisplayedinacommercialandhewillearn140 every time one of his songs is played in a movie, so his total earnings are
140M+50C=770140M+50C=770
We have a system of linear equations that can be easily solved by using the formula for C in the above equation
140M+50(M+4)=770140M+50(M+4)=770
Operating
140M+50M+200=770140M+50M+200=770
Reducing
190M=770-200=570190M=770−200=570
Solving
M=570/190=3M=570/190=3
The number of commercials is
C=M+4=7C=M+4=7
Owen's songs were played on 3 movies and on 7 commercials.