Find the price of an adult ticket And the price of a student ticket.

Question

The school that Ryan goes to is selling tickets to a spring musical. On the first day of ticket salesthe school sold 2 adult tickets and 11 student tickets for a total of $172. The school taken $68 on the second day by selling 6 adult tickets and 1 student ticket. Find the price of an adult ticket

and the price of a student ticket.

Answer 1

Hi Michelle

Adult tickets are $9

Student tickets are $14

A system of equations will work for this situation

Let x = adult tickets

Let y = student tickets

Equation 1 = sales for day 1

2x + 11y = 172

Equation 2 = sales for day 2

6x + y = 68

We can eliminate x by multiplying Equation 1 by negative 3, then combining it with Equation 2

-6x - 33y = -516

6x + y = 68

This combination eliminates x leaving

-32y = -448

y = -448/-32

y = 14 so student tickets cost $14

We can go back to any of our original equations and solve for x, I will use Equation 2

6x + y = 68

6x + 14 = 68

6x = 68 - 14

6x = 54

x = 54/6

x = 9 so adult tickets cost $9

We can check everything in both Equations

2(9) + 11(14) = 172

18 + 154 = 172

6(9) + 14 = 68

54 + 14 = 68

I hope you find this useful if you have any questions send me a message.