Qasim is a songwriter who collects royalties on his songs whenever they are played in a commercial or a movie. Qasim will earn $40 every time one of his songs is played in a commercial and he will earn $140 every time one of his songs is played in a movie. Qasim's songs were played on 5 more commercials than movies, and his total earnings on the royalties from all commercials and movies was $560. Graphically solve a system of equations in order to determine the number of commercials, x, commax, and the number of movies, y, commay, on which Qasim's songs were played
use system of equations and plot all coordinates
Let's assume the number of commercials is x and the number of movies is y.
According to the given information, Qasim earns $40 every time one of his songs is played in a commercial and $140 every time one of his songs is played in a movie.
Therefore, the total earnings from commercials (x) and movies (y) can be expressed as:
Total earnings from commercials = $40 * x
Total earnings from movies = $140 * y
It is also given that Qasim's songs were played on 5 more commercials than movies:
x = y + 5
And the total earnings from all commercials and movies is $560:
$40 * x + $140 * y = $560
Now, we can solve this system of equations.
Substitute the value of x from the first equation into the fourth equation:
$40 * (y + 5) + $140 * y = $560
$40y + $200 + $140y = $560
$180y + $200 = $560
$180y = $360
y = 2
Substitute the value of y = 2 into the third equation:
x = y + 5
x = 2 + 5
x = 7
So, the number of commercials, x, is 7 and the number of movies, y, is 2.
The coordinates of the solution are (7, 2).
Now, let's plot these coordinates on a graph:
x-axis represents the number of commercials (x)
y-axis represents the number of movies (y)
The point (7, 2) can be plotted as the intersection of the lines x = 7 and y = 2.
The graph should look like this:
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y=2 |
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|_ _ _._ _ _ _ _ _ _ _ _ _ _x=7
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So, the number of commercials, x, is 7 and the number of movies, y, is 2.