(x,y) of the solution to the system of equations, where x represents the number of commercials and y represents the number of movies on which Gianna's songs were played.
The system of equations can be expressed as follows:
1) x + y = total number of songs played (equation relating the total number of songs played)
2) 50x + 100y = total earnings from royalties (equation relating the total earnings)
Since we know that Gianna's songs were played on twice as many commercials as movies, we can also express this relationship as:
3) x = 2y (equation relating the number of commercials and movies)
Solving the system of equations, we can substitute equation 3 into equations 1 and 2:
1) (2y) + y = total number of songs played
=> 3y = total number of songs played
=> y = (1/3) * (total number of songs played)
2) 50(2y) + 100y = total earnings from royalties
=> 100y + 100y = total earnings from royalties
=> 200y = total earnings from royalties
=> y = (1/200) * (total earnings from royalties)
Substituting back into equation 1, we have:
(2y) + y = (1/3) * (total number of songs played)
=> 3y = (1/3) * (total number of songs played)
=> y = (1/9) * (total number of songs played)
Therefore, the coordinates (x,y) of the solution to the system of equations are:
(x, y) = (2y,y) = (2(1/9)*(total number of songs played), (1/9)*(total number of songs played))
Since the total earnings from royalties was $800, the total number of songs played can be determined by dividing the total earnings by $50 (since each commercial earns $50):
(total number of songs played) = (total earnings from royalties) / $50
= $800 / $50
= 16
Substituting this value into the coordinates, we have:
(x, y) = (2(1/9)*16, (1/9)*16)
= (32/9, 16/9)
Gianna is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Gianna will earn $50 every time one of her songs is played in a commercial and she will earn $100 every time one of her songs is played in a movie. Gianna's songs were played on twice as many commercials as movies and her total earnings on the royalties from all commercials and movies was $800. Graphically solve a system of equations in order to determine the number of commercials, x, and the number of movies, y, on which Gianna's songs were played.
Give the coordinates
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Are you sure this is right?
Apologies for the previous incorrect response. Let's solve the system of equations correctly:
1) x + y = total number of songs played
2) 50x + 100y = total earnings from royalties
3) x = 2y
First, substitute equation 3 into equation 1:
2y + y = total number of songs played
3y = total number of songs played
y = (1/3) * (total number of songs played)
Next, substitute y back into equation 3:
x = 2 * (1/3) * (total number of songs played)
x = (2/3) * (total number of songs played)
Now, substitute x and y back into equation 2 to solve for the total earnings from royalties:
50((2/3) * (total number of songs played)) + 100((1/3) * (total number of songs played)) = total earnings from royalties
Simplifying:
(100/3) * (total number of songs played) + (100/3) * (total number of songs played) = total earnings from royalties
(200/3) * (total number of songs played) = total earnings from royalties
Given that the total earnings from royalties was $800, we can set up the equation:
(200/3) * (total number of songs played) = 800
Solving for the total number of songs played:
total number of songs played = (3/200) * 800
total number of songs played = 12
Finally, substitute this value back into the equations for x and y:
x = (2/3) * 12 = 8
y = (1/3) * 12 = 4
Therefore, the solution to the system of equations is (x, y) = (8, 4). Gianna's songs were played on 8 commercials and 4 movies.
1) x + y = total number of songs played
2) 50x + 100y = total earnings from royalties
3) x = 2y
First, substitute equation 3 into equation 1:
2y + y = total number of songs played
3y = total number of songs played
y = (1/3) * (total number of songs played)
Next, substitute y back into equation 3:
x = 2 * (1/3) * (total number of songs played)
x = (2/3) * (total number of songs played)
Now, substitute x and y back into equation 2 to solve for the total earnings from royalties:
50((2/3) * (total number of songs played)) + 100((1/3) * (total number of songs played)) = total earnings from royalties
Simplifying:
(100/3) * (total number of songs played) + (100/3) * (total number of songs played) = total earnings from royalties
(200/3) * (total number of songs played) = total earnings from royalties
Given that the total earnings from royalties was $800, we can set up the equation:
(200/3) * (total number of songs played) = 800
Solving for the total number of songs played:
total number of songs played = (3/200) * 800
total number of songs played = 12
Finally, substitute this value back into the equations for x and y:
x = (2/3) * 12 = 8
y = (1/3) * 12 = 4
Therefore, the solution to the system of equations is (x, y) = (8, 4). Gianna's songs were played on 8 commercials and 4 movies.
can you give me the coordinates to plot
Apologies for the confusion earlier. The correct coordinates to plot are:
(x, y) = (8, 4)
The x-coordinate represents the number of commercials played (8) and the y-coordinate represents the number of movies played (4).
(x, y) = (8, 4)
The x-coordinate represents the number of commercials played (8) and the y-coordinate represents the number of movies played (4).
can you give the line coordinates that intercept
Certainly! The line coordinates that intercept are:
The x-intercept is when the y-coordinate is 0:
(x, y) = (8, 0)
The y-intercept is when the x-coordinate is 0:
(x, y) = (0, 4)
These points represent the intersections of the line with the x-axis (x-intercept) and y-axis (y-intercept).
The x-intercept is when the y-coordinate is 0:
(x, y) = (8, 0)
The y-intercept is when the x-coordinate is 0:
(x, y) = (0, 4)
These points represent the intersections of the line with the x-axis (x-intercept) and y-axis (y-intercept).
give me the coordinates the intersect (8,4)
I apologize for the confusion. The coordinates you requested are the coordinates of the point of intersection between the line and the axes.
The coordinates of the point of intersection with the x-axis (x-intercept) are:
(x, y) = (8, 0)
The coordinates of the point of intersection with the y-axis (y-intercept) are:
(x, y) = (0, 4)
These points represent the intersections of the line with the x-axis and y-axis. The given point (8, 4) does not represent an intersection with the axes. I apologize for any misunderstanding caused.
The coordinates of the point of intersection with the x-axis (x-intercept) are:
(x, y) = (8, 0)
The coordinates of the point of intersection with the y-axis (y-intercept) are:
(x, y) = (0, 4)
These points represent the intersections of the line with the x-axis and y-axis. The given point (8, 4) does not represent an intersection with the axes. I apologize for any misunderstanding caused.
1 answer