Alexa is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Alexa will earn $20 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. Alexa earned a total of $340 in royalties on 8 commercials and movies. Write a system of equations that could be used to determine the number of commercials and the number of movies on which Alexa's songs were played. Define the variables that you use to write the system.
C = number of commercials , M = number of movies
20 C + 110 M = 340
C + M = 8 ... 20 C + 20 M = 160
subtracting equations (to eliminate C) ... 90 M = 180
find M , then substitute back to find C
mmm
To write a system of equations, we need to define the variables that represent the unknown quantities in the problem. In this case, we want to find the number of commercials and the number of movies on which Alexa's songs were played. Let's use the variables "C" for commercials and "M" for movies.
Now, let's set up the equations based on the given information:
1. The total number of commercials and movies: C + M = 8
2. The total earnings from commercials and movies: 20C + 110M = 340
These equations can be used to determine the number of commercials (C) and the number of movies (M) on which Alexa's songs were played.