Final answer:
To determine the number of adult and student tickets purchased, we solved a system of two equations based on the given prices and total spent. The solution shows that Mr. Steele bought 8 student tickets and no adult tickets for a total of $32.
Step-by-step explanation:
The question revolves around solving a system of linear equations to determine how many adult and student tickets Mr. Steele purchased from the Arcadia Theater. We are told that adult tickets cost $3 and student tickets cost $4, and that Mr. Steele bought a total of 8 tickets for $32. We can let the number of adult tickets be a and the number of student tickets be s. This gives us two equations:
- a + s = 8 (because he bought 8 tickets in total)
- 3a + 4s = 32 (because the tickets cost $32 in total)
By solving this system of equations, we can find the values of a and s. Multiplying the first equation by 3 gives us 3a + 3s = 24. Subtracting this from the second equation cancels out the a, leaving us with s = 32 - 24, which simplifies to s = 8. This means he bought 8 student tickets and 0 adult tickets. The important conclusion to note is that Mr. Steele did not purchase any adult tickets. This took into account the prices of the tickets and the total amount spent.