Georgia Connections Academy is selling tickets to its Spring Fling. Adult tickets cost $4 and student tickets cost $2.50. The school makes $2,820. Write an equation that represents this situation to find the cost of all adult and student tickets sold. Use the variable s for student tickets and a for adult tickets sold.
(7 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Write an equation that represents this situation to find the cost of all adult and student tickets sold. Use the variable s for student tickets and a for adult tickets sold.
Response area a + Response area s = Response area
900 tickets are sold for the spring fling. Write an equation to represent this situation.
a + Response area = Response area
Use the above system of equations to determine how many adult and student tickets were sold.
Response area adult tickets and Response area student tickets were sold.
:: 2820
:: a
:: 380
:: 2.50
:: 591
:: 520
:: 900
:: 6.5
:: 4
:: s
:: 309
:: 390
The equation that represents the cost of all adult and student tickets sold is:
4a + 2.50s = 2820
The equation that represents the number of tickets sold is:
a + s = 900
Using the above system of equations, we can solve for the values of adult tickets and student tickets sold:
adult tickets sold = 520
student tickets sold = 380
are you sure??
Apologies for the confusion. Let's go through the steps again:
The equation that represents the cost of all adult and student tickets sold is:
4a + 2.50s = 2820
The equation that represents the number of tickets sold is:
a + s = 900
Using the above system of equations, we can solve for the values of adult tickets and student tickets sold:
Multiplying the second equation by 2.50:
2.50a + 2.50s = 2250
Subtracting the second equation from the first equation:
(4a + 2.50s) - (2.50a + 2.50s) = 2820 - 2250
1.50a = 570
a = 380
Substituting the value of a into the second equation:
380 + s = 900
s = 520
Therefore, 380 adult tickets and 520 student tickets were sold.
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Question
Use the image to answer the question.
A coordinate plane with 4 quadrants ranges from negative 10 to 10 in unit increments on both the x and y axes. A solid line and a dashed line with arrows at both the ends are drawn parallel to each other on the graph. The equation of the solid line is y equals negative x plus 3. The equation of the dashed line is x plus y equals 8.
Solving the system y=−x+3 and x+y=8 by graphing shows that there is no solution to the system. Is this statement true or false? Explain.
(1 point)
Responses
The statement is true, because the lines are parallel.
The statement is true, because the lines are parallel.
The statement is false, because the lines are parallel.
The statement is false, because the lines are parallel.
The statement is false, because the lines have an intersection point.
The statement is false, because the lines have an intersection point.
The statement is true, because the lines have an intersection point.
The statement is true, because the lines have an intersection point.
The statement is false, because the lines have an intersection point.
By graphing the equations y = -x + 3 and x + y = 8, we can see that the solid line and dashed line intersect at a single point. This means that there is a solution to the system of equations, contradicting the statement that there is no solution. Therefore, the statement is false.
is that true???
Apologies for the confusion. Let's go through the steps again:
The given equations are:
y = -x + 3 (Solid line)
x + y = 8 (Dashed line)
To solve the system of equations, we can set the two equations equal to each other:
-x + 3 = 8 - x
Simplifying, we find:
3 = 8
This is not a true statement, which means the lines are parallel and do not intersect. Therefore, the statement is true, as the system of equations has no solution.
Use the image to answer the question.
A coordinate plane with 4 quadrants ranges from negative 10 to 10 in unit increments on both the x and y axes. A solid line and a dashed line with arrows at both the ends are drawn parallel to each other on the graph. The solid line passes through left parenthesis 0 comma 2 right parenthesis and left parenthesis 2 comma 0 right parenthesis. The dashed line passes through left parenthesis negative 7 comma 0 right parenthesis and left parenthesis 7 comma 0 right parenthesis.
Does the graph show the system of equations x+y=2 and −x+y=7? Should the lines for the system be parallel?
(1 point)
Responses
The graph of x+y=2 is incorrect. The lines should intersect.
The graph of x plus y equals 2 is incorrect. The lines should intersect.
Both graphs are correct. The lines should be parallel.
Both graphs are correct. The lines should be parallel.
The graph of −x+y=7 is incorrect. The lines should be parallel.
The graph of negative x plus y equals 7 is incorrect. The lines should be parallel.
The graph of −x+y=7 is incorrect. The lines should intersect.
The graph of negative x plus y equals 7 is incorrect. The lines should intersect.
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The correct response is:
The graph of x+y=2 is incorrect. The lines should intersect.
The graph of −x+y=7 is incorrect. The lines should be parallel.
The lines for the system of equations x+y=2 and −x+y=7 should not be parallel. They should intersect at a single point. However, based on the given information, the lines on the graph are parallel and do not intersect. Therefore, the graph does not show the system of equations x+y=2 and −x+y=7 correctly.