Tickets to a movie cost $7.25 for adults and $5.50 for students. A group of friends purchased 8 tickets for $52.75. How many adult tickets and student tickets were purchased?

Have you tried using algebra?

A + S = 8

725 A + 550 S = 5275

Solve those equations for A and S.

Hint: subsitute 8-S for A in the second equation

To solve this problem, we can set up a system of equations. Let's say that the number of adult tickets purchased is represented by 'a', and the number of student tickets purchased is represented by 's'.

Given that the cost of an adult ticket is $7.25 and the cost of a student ticket is $5.50, we can write the following equation for the total cost of the tickets:

7.25a + 5.50s = 52.75 (Equation 1)

We also know that a group of friends purchased a total of 8 tickets, so the number of adult tickets and student tickets must add up to 8:

a + s = 8 (Equation 2)

We can solve this system of equations using different methods, such as substitution or elimination. I will demonstrate the method of substitution here:

From Equation 2, we can express 'a' in terms of 's' as:
a = 8 - s

Now, we substitute this expression for 'a' into Equation 1:

7.25(8 - s) + 5.50s = 52.75

Expanding and simplifying this equation gives us:
58 - 7.25s + 5.50s = 52.75

Combining like terms:
-1.75s = -5.25

Dividing both sides by -1.75:
s = 3

Now, substitute the value of 's' back into Equation 2 to find the value of 'a':
a + 3 = 8

Subtracting 3 from both sides:
a = 5

Therefore, 5 adult tickets and 3 student tickets were purchased.