Nakeisha is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Nakeisha 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. Nakeisha's songs were played on 2 more commercials than movies, and her total earnings on the royalties from all commercials and movies was $760. Write a system of equations that could be used to determine the number of commercials and the number of movies on which Nakeisha's songs were played. Define the variables that you use to write the system.

Question

Nakeisha is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Nakeisha 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. Nakeisha's songs were played on 2 more commercials than movies, and her total earnings on the royalties from all commercials and movies was $760. Write a system of equations that could be used to determine the number of commercials and the number of movies on which Nakeisha's songs were played. Define the variables that you use to write the system.

Answer 1

Let c be the number of commercials on which Nakeisha's songs were played and m be the number of movies on which Nakeisha's songs were played.

The first equation is c = m + 2, as Nakeisha's songs were played on 2 more commercials than movies.
The second equation is 30c + 110m = 760, as Nakeisha's total earnings on the royalties from all commercials and movies was $760. Answer: $\begin{cases} c=m+2 \\ 30c+110m=760 \end{cases}$