Question

Carter is a songwriter who collects royalties on his songs whenever they are played in a commercial or a movie. Carter will earn $50 every time one of his songs is played in a commercial and he will earn $130 every time one of his songs is played in a movie. Carter earned a total of $1000 in royalties on 12 commercials and movies. Determine the number of commercials and the number of movies on which Carter's songs were played.

Answer 1

Number of songs played in commercial are 7 and Number of songs played in movie are 5.

Explanation:

Let Number of songs played in commercial be x

and Number of songs played in movie be y.

Total number of songs played =12

Hence,

`x+y=12\ \ \ \ equation \ 1`

Also

Cost for songs played in commercial = $50

Cost for songs played in movie = $130

Total Money earned = $1000

Hence,

`\$50x+\$130y=\$1000`

Dividing by 10 on both side we get;

`\$5x+\$13y=\$100\ \ \ \ equation \ 2`

Now multiplying equation 1 by 5 we get;

`5x+5y=60 \ \ \ \ equation \ 3`

Now Subtracting equation 3 from equation 2 we get;

`(5x+13y=100)- (5x+5y=60)\\8y=40\\y=(40)/(8)=5`

y = 5

x + y = 12

x + 5 = 12

x = 12 - 5

x = 7

Hence, Number of songs played in commercial are 7 and Number of songs played in movie are 5.