Final answer:
To find out how many adult tickets the theater sold last night, we can set up an equation using the given information. By solving this equation, we can determine that the theater sold 149 adult tickets.
Step-by-step explanation:
To solve this problem, let's assume that the number of adult tickets sold is 'x'. Since we know that the total number of tickets sold is 312, we can find the number of child tickets sold by subtracting 'x' from 312. Now, the total revenue from adult tickets can be calculated by multiplying the number of adult tickets sold by the price per adult ticket, which is $17. Similarly, the total revenue from child tickets can be calculated by multiplying the number of child tickets sold by the price per child ticket, which is $4. We also know that the total revenue from both types of tickets is $3185. Setting up an equation using the given information, we get:
17x + 4(312 - x) = 3185
Simplifying the equation:
17x + 1248 - 4x = 3185
Combining like terms:
13x + 1248 = 3185
Subtracting 1248 from both sides:
13x = 1937
Dividing both sides by 13:
x = 149
Therefore, the theater sold 149 adult tickets last night.