Question

Sadie is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Sadie will earn $40 every time one of her songs is played in a commercial and she will earn $120 every time one of her songs is played in a movie. Sadie's songs were played on 3 more commercials than movies, and her total earnings on the royalties from all commercials and movies was $440. Write a system of equations that could be used to determine the number of commercials and the number of movies on which Sadie's songs were played. Define the variables that you use to write the system.

Answer 1

5 commercials and 2 movies

Explanation:

x being number of commercials and y being number of movies

40x + 120y = 440

y + 3 = x

120 x 2 = 240

40 x 5 = 200

40(5) x 120(2) = 440

200 + 240 = 440

440 = 440

Answer 2

To solve this problem, we can define the following variables:

c: The number of commercials on which Sadie's songs were played
m: The number of movies on which Sadie's songs were played

With these variables, we can write the following system of equations:

c + m = t (1)
40c + 120m = 440 (2)

Where t represents the total number of commercials and movies on which Sadie's songs were played.

Equation (1) represents the total number of commercials and movies on which Sadie's songs were played, and equation (2) represents the total earnings from all commercials and movies.

To solve this system of equations, we can substitute the value for c in equation (1) into equation (2) to eliminate c. This gives us the following equation:

40(t - m) + 120m = 440
40t - 40m + 120m = 440
40t = 480
t = 12

Substituting this value for t back into equation (1) gives us the following equation:

c + m = 12

We can solve this equation to find the number of commercials and movies on which Sadie's songs were played. For example, if c represents the number of commercials, then m = 12 - c. If c = 5, then m = 7, and if c = 7, then m = 5.

Thus, the number of commercials and movies on which Sadie's songs were played can be represented by the system of equations:

c + m = 12
40c + 120m = 440

where c represents the number of commercials and m represents the number of movies.