Use your graphing calculator: Desmos Graphing Calculator Link%0D%0A%0D%0AGeorgia 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. %0D%0A%0D%0A(7 points)%0D%0APut 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.%0D%0AWrite 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.%0D%0A%0D%0A Response area a + Response area s = Response area%0D%0A%0D%0A900 tickets are sold for the spring fling. Write an equation to represent this situation.%0D%0A%0D%0Aa + Response area = Response area%0D%0A%0D%0AUse the above system of equations to determine how many adult and student tickets were sold.%0D%0A%0D%0AResponse area adult tickets and Response area student tickets were sold.%0D%0A%0D%0A309390380510520as5912.50282090046.5
To find the equation that represents the cost of all adult and student tickets sold, we can use the given information that adult tickets cost $4 and student tickets cost $2.50. Let's set up the equation:
4a + 2.50s = 2820
Next, let's write an equation to represent the situation where 900 tickets were sold:
a + s = 900
To determine how many adult and student tickets were sold, we can solve this system of equations.
Please note that the response area "adult tickets and student tickets were sold" seems to be cut off and does not provide the complete information.
To find the equation representing the cost of all adult and student tickets sold, we can use the information given:
Adult tickets cost $4, so the cost of adult tickets sold is 4a.
Student tickets cost $2.50, so the cost of student tickets sold is 2.50s.
The total revenue from ticket sales is $2,820.
We can set up the following equation:
4a + 2.50s = 2820
To find the equation representing the number of tickets sold, we know that 900 tickets were sold in total. So, we have:
a + s = 900
To solve this system of equations, we can use the substitution method or the elimination method. Let's use the elimination method:
Multiply the second equation by -4 to make the coefficients of "a" add up to zero:
-4(a + s) = -4(900)
-4a - 4s = -3600
Now, we can add the modified equations together to eliminate the "a" term:
4a + 2.50s + (-4a - 4s) = 2820 + (-3600)
-1.50s = -780
s = -780 / -1.50
s = 520
Substitute the value of s back into one of the original equations to find the value of a:
a + 520 = 900
a = 900 - 520
a = 380
Therefore, 380 adult tickets and 520 student tickets were sold.
To solve this problem using a graphing calculator, follow these steps:
1. Go to the Desmos Graphing Calculator link provided.
2. In the input area, type the equation for the cost of all adult and student tickets sold: `a + s = 2,820`. This equation represents the total revenue generated from ticket sales, where 'a' represents the number of adult tickets sold and 's' represents the number of student tickets sold. Press Enter or click outside the input area to graph the equation.
3. To represent the equation for the number of tickets sold, use the information given that 900 tickets were sold for the Spring Fling. In the input area, type `a + s = 900`. This equation represents the total number of tickets sold, where 900 is the sum of adult and student tickets. Press Enter or click outside the input area to graph the equation.
4. Now we have a system of equations with two unknowns: `a + s = 2,820` and `a + s = 900`. The next step is to determine the points of intersection, which represent the solution to the system.
5. Look for the points of intersection on the graph. These points represent the combination of adult and student tickets sold that satisfy both equations.
6. In the response area for the number of adult and student tickets sold, input the values of 'a' and 's' at the point of intersection. For example, if the point of intersection is (350, 550), then input '350' in the response area for adult tickets and '550' in the response area for student tickets.