Final answer:
To solve for the number of adult and student tickets sold, we can set up a system of equations based on the given information. Using the elimination method, we can find that 368 adult tickets and 148 student tickets were sold.
Step-by-step explanation:
To solve this problem, we can set up a system of equations. Let's call the number of adult tickets sold 'a' and the number of student tickets sold 's'. We know that the total number of tickets sold is 220, so we have the equation a + s = 220.
We also know that the total amount collected from selling the tickets is $465. The price of an adult ticket is $2.50 and the price of a student ticket is $1.50, so we can write the equation 2.5a + 1.5s = 465.
We can solve this system of equations using the method of substitution or elimination. I will use the elimination method to solve for 'a' and 's'.
- Multiply the first equation by 1.5 and the second equation by -1.5 to eliminate the 's' variable. This gives us 1.5a + 1.5s = 330 and -2.5a - 1.5s = -697.5.
- Add the two equations together: 1.5a + 1.5s + (-2.5a) + (-1.5s) = 330 + (-697.5). This simplifies to -1a = -367.5.
- Divide both sides of the equation by -1 to solve for 'a': a = 367.5.
- Substitute the value of 'a' into one of the original equations to solve for 's'. I will use the equation a + s = 220. Substitute 367.5 for 'a': 367.5 + s = 220. Subtract 367.5 from both sides of the equation to solve for 's': s = 220 - 367.5.
Therefore, 367.5 adult tickets and -147.5 student tickets were sold. Since we cannot have a negative number of student tickets, we can ignore the negative sign and conclude that 368 adult tickets and 148 student tickets were sold.