Question

Emily is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Emily will earn $50 every time one of her songs is played in a commercial and she will earn $150 every time one of her songs is played in a movie. Emily's songs were played on 3 times as many commercials as movies and her total earnings on the royalties from all commercials and movies were $600. Graphically solve a system of equations in order to determine the number of commercials, x,x, and the number of movies, y,y, on which Emily's songs were played.

Answer 1

Answer:

(6,2)

Step-by-step explanation:

Variable Definitions:

​x= the number of commercials

y= the number of movies

Each commercial earns Emily $50, so x commercials would earn her 50x dollars in royalties. Each movie earns Emily $150, so y movies would earn her 150y dollars in royalties. Therefore, the total royalties 50x+150y equals $600:

50x+150y=600

Since Emily's songs were played on 3 times as many commercials as movies, if we multiply 3 by the number of movies, we will get the number of commercials, meaning x equals 3y.

x=3y

Write System of Equations:

​50x+150y=600

x=3y

Solve for y in each equation:

1)  50x+150y=600

   150y=−50x+600

   y=-1/3x+4

2)  x=3y

    y=1/3x

The x variable represents the number of commercials and the yy variable represents the number of movies. Since the lines intersect at the point (6,2) we can say:

Emily's songs were played on 6 commercials and 2 movies.

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