The school that Jill goes to is selling tickets to fall musical. On the first day of ticket sales the school sold 2 senior citizen tickets and 5 student tickets for a total of $50.12 the school took in $78.12 on the second day by selling 6 senior or citizen tickets and 3 student tickets. Find the price of a senior citizen ticket and the price of a student ticket.

The price of senior citizen ticket is $10.01 and the price of student ticket is $6.02.

Step-by-step explanation:

Let the price of senior citizen ticket be $x

and the price of student ticket be $y.

Now, from the question

The school sold 2 senior citizen tickets and 5 student tickets for a total of $50.12. That is

2x + 5y = 50.12 (1)

Also from the question,

The school took in $78.12 by selling 6 senior or citizen tickets and 3 student tickets. That is

6x + 3y = 78.12 (2)

Now, we will bring the two equations together and solve simultaneously

2x + 5y = 50.12 (1)

6x + 3y = 78.12 (2)

From equation (2)

6x + 3y = 78.12 (2)

Make y the subject of the formula

Then,

3y = 78.12 - 6x

∴y = 26.04 - 2x (3)

Substitute the value of y into equation (1)

2x + 5y = 50.12 (1)

2x + 5(26.04-2x) = 50.12

2x + 130.2 - 10x = 50.12

Collect like terms

2x - 10x = 50.12 - 130.2

-8x = -80.08

8x = 80.08

x = 80.08 / 8

x = 10.01

Now, to determine y, substitute the value of x into equation (3)

y = 26.04 - 2x

y = 26.04 -2(10.01)

y = 26.04 - 20.02

y = 6.02

∴ x = 10.01; y = 6.02

Recall that, the price of senior citizen ticket is $x and the price of student ticket is $y.

Hence, the price of senior citizen ticket is $10.01 and the price of student ticket is $6.02.