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

Answer:

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

Step-by-step 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;

$(5x+13y=100)- (5x+5y=60)\\8y=40\\y=\frac{40}{8}=5$

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.