The Montague family and their neighbors the Capulets attended the school play together. The Montagues bought two adult tickets and three student tickets for $16. The Capulets purchased three adult tickets and two student tickets for $19. How much was each adult and student ticket?

The cost for adult tickets be represented by x = $5

The cost for student tickets be y = $2

Step-by-step explanation:

Let the cost for adult tickets be represented by x

the cost for student tickets be y

The Montague family and their neighbors the Capulets attended the school play together. The Montagues bought two adult tickets and three student tickets for $16.

= 2x + 3y = 16... Equation 1

The Capulets purchased three adult tickets and two student tickets for $19.

3x + 2y = 19 Equation 2

How much was each adult and student ticket?

2x + 3y = 16... Equation 1

3x + 2y = 19 Equation 2

We solve using Elimination method

Multiply Equation 1 by 2 and Equation 2 by 3 to eliminate u

4x + 6y = 32 Equation 3

9x + 6y = 57 Equation 4

Subtract Equation 4 from 3

-5x = -25

x = 25/5

x = $5

2x + 3y = 16... Equation 1

Since x = $5

2($5) + 3y = 16

10 + 3y = 16

3y = 16 - 10

3y = 6

y = 6/3

y = $2

Therefore:

The cost for adult tickets be represented by x = $5

The cost for student tickets be y = $2