Student tickets to the Homecoming game cost $5 each. General admission tickets cost $8 each. So far, 150 tickets have been sold. $900 has been collected.
A. Write a system of equations for this model in standard form.
8G = General Admissions: 50 sold
5S = Student tickets: 100 sold
Equation 1: S+G = 150 (100) + (50) = 150
Equation 2: 5S+8G=900
S = 150 – G
8G + 5(150 – G) = 900
8G – 5G + 750 = 900
3G = 150
G = 50
Need help checking and help with equation 2
B. Graph the system. ( let each square represents 20 units)
C. What is the solution to the system?
D. Is (180, -30) a solution? Explain.
Are (50) and (100) the correct coordinates? just double checking.
your equations are correct
your solution is correct
D is of course, not a solution. Not only does 5*180+8(-30)≠900, but -30 is not a valid number of tickets.
A. To write a system of equations for this model in standard form, we can let S represent the number of student tickets sold and G represent the number of general admission tickets sold.
We know that 150 tickets have been sold, so we can write the equation: S + G = 150.
We also know that the total amount collected from ticket sales is $900. Since each student ticket costs $5 and each general admission ticket costs $8, the equation for the total collected amount is: 5S + 8G = 900.
B. To graph the system, we can create a coordinate plane where the x-axis represents the number of student tickets sold (S) and the y-axis represents the number of general admission tickets sold (G). Each square on the graph can represent 20 units, so we can label the x-axis from 0 to 100 and the y-axis from 0 to 60.
C. To find the solution to the system, we need to solve it. We can use the substitution method to solve the system of equations.
From Equation 1: S + G = 150,
we can solve for S in terms of G: S = 150 - G.
Substituting this value of S into Equation 2: 5S + 8G = 900,
we get: 5(150 - G) + 8G = 900.
Simplifying, we have: 750 - 5G + 8G = 900,
which further simplifies to: 3G = 150.
Dividing both sides by 3, we find: G = 50.
Now, substitute this value of G into Equation 1 to solve for S:
S + 50 = 150,
which gives us: S = 100.
Therefore, the solution to the system is S = 100 and G = 50.
D. Let's check if (180, -30) is a solution.
According to the system of equations, S represents the number of student tickets sold and G represents the number of general admission tickets sold. Both S and G must be non-negative numbers since they represent the quantity of tickets sold.
In the case of (180, -30), the number of student tickets sold is 180 and the number of general admission tickets sold is -30. Since the number of general admission tickets sold cannot be negative, (180, -30) is not a valid solution to the system.