Final answer:
To determine the number of adult and student tickets sold, two equations are set up using variables x for adult tickets and y for student tickets. Solving the system of equations shows that 55 adult tickets and 25 student tickets were sold.
Step-by-step explanation:
To solve for the number of adult and student tickets sold when 80 tickets were presold for a musical, generating a revenue of $860, with adults paying $12 and students $8, we can set up a system of equations using two variables. Let's define x to be the number of adult tickets sold and y to be the number of student tickets sold.
The first equation comes from the total number of tickets sold: x + y = 80. The second equation comes from the total revenue generated: 12x + 8y = $860.
Now we can solve the system of equations. Multiplying the first equation by 8 (to align the 'y' coefficients), we get 8x + 8y = 640. Subtract this new equation from the revenue equation to eliminate 'y': (12x + 8y) - (8x + 8y) = 860 - 640, which simplifies to 4x = 220. Dividing by 4 gives us x = 55, meaning 55 adult tickets were sold.
The last step is to solve for 'y'. Substituting x into the first equation: 55 + y = 80, we find that y = 25, which means 25 student tickets were sold.
In conclusion, 55 adult tickets and 25 student tickets were sold to the musical.