Answer:
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.
