The photography club decided to go on a field trip to the Andy Warhol museum. They had to break into smaller groups once they got there. The first group had 25 students and 2 teachers. Their cost was $97.50. The second group had 32 students and 3 teachers. Their cost was $127. What is the cost of each student and each teacher?

Part A: Define your variables

Part B: Write a system of equations to represent this situation

Part C: Solve the system of equations you wrote in Part B.

Part D: Interpret what your answer means in context to this situation.

A)
Let x represent the cost of 1 student, and y the cost of 1 teacher.

B)
In the first group, there's 25 students and 2 teachers. Their total cost is $97.50
So 25x + 2y = 97.50
In the second group, there's 32 students and 3 teachers. Their total cost is $127
So 32x + 3y = 127

We get the following system of equations:
25x + 2y = 97.50 (1)
32x + 3y = 127 (2)

C)
25x + 2y = 97.50 (1)
32x + 3y = 127 (2)

In equation (1)
25x + 2y = 97.50
25x + 2y - 2y = 97.50 - 2y
25x = 97.50 - 2y
25x / 25 = 97.50/25 - 2y/25
x = 3.9 - (2/25)y

In equation (2), let's replace x by its algebraic value
32x + 3y = 127
32(-2/25y + 3.9) + 3y = 127
11/25y + 124.8 = 127
11/25y + 124.8 - 124.8 = 127 - 124.8
11/25y = 2.2
(11/25y) / (11/25) = 2.2 / (11/25)
y = 5

x = -2/25y + 3.9
x = -2/25 * 5 + 3.9
x = 3.5

So the cost of each student is $3.5, and the cost of each teacher is $5.

Hope this helps! :)