Final answer:
To find the price of the student ticket, set up a system of equations using the given information. Solve the system of equations to find the price of the student ticket.
Step-by-step explanation:
To find the price of the student ticket, we need to set up a system of equations using the given information.
Let's denote the price of a student ticket as 's' and the price of a general admission ticket as 'g'.
From the first night's ticket sales, we know that 70 student tickets and 160 general admission tickets were sold, resulting in a total sales of $1790. This can be represented as the equation 70s + 160g = 1790.
From the second night's ticket sales, we know that 130 student tickets and 110 general admission tickets were sold, resulting in a total sales of $1640. This can be represented as the equation 130s + 110g = 1640.
We can solve this system of equations to find the price of the student ticket.
By multiplying the first equation by 13 and the second equation by 7, we can eliminate the g variable when adding the two equations together.
After simplifying, we get 910s + 2080g = 23370. Substituting this result into the equation 130s + 110g = 1640, we can solve for s.
130s + 110g = 1640 becomes 130s + 110(23370 - 910s)/2080 = 1640.
Simplifying this equation gives us the value of s.
s = $6.50