How much did the student tickets for both classes cost in total?

Steps to Solve

1. Set Up Variables
   Define the variables needed for the equations:
   Let ( x ) be the cost of a student ticket and ( y ) be the cost of an adult ticket.

2. Set Up the Equations
   From the information given:

• For Ms. Green:
  ( 28x + 4y = 262 )
• For Mr. White:
  ( 22x + 2y = 191 )

3. Solve the Equations
   We can solve this system of equations using any preferred method. Here, we will use the elimination method.
   First, let's multiply the second equation by 2 to align coefficients:
   $$ 44x + 4y = 382 $$

4. Subtract the First Equation
   Now, subtract the first equation from the modified second equation:
   $$ (44x + 4y) - (28x + 4y) = 382 - 262 $$
   This simplifies to:
   $$ 16x = 120 $$

5. Solve for ( x )
   Divide both sides by 16:
   $$ x = \frac{120}{16} = 7.5 $$
   Thus, the cost of a student ticket is $7.50.

6. Substitute to Find ( y )
   Substitute ( x ) back into one of the original equations to find ( y ). Using Ms. Green's equation:
   $$ 28(7.5) + 4y = 262 $$
   Calculating gives:
   $$ 210 + 4y = 262 $$
   $$ 4y = 52 $$
   $$ y = \frac{52}{4} = 13 $$
   Thus, the cost of an adult ticket is $13.

7. Calculate Total Cost of Student Tickets
   Now calculate the total number of student tickets purchased:
   $$ 28 + 22 = 50 $$
   Total cost for student tickets:
   $$ 50 \times 7.5 = 375 $$