Answer:
Price of the adult ticket is $13
Price of the child ticket is $3
Step-by-step explanation:
Lets x be the adult ticket and y be the child ticket.
Given:
School sold 14 adult tickets and 14 child tickets for a total of $224, so the first equation is.
-------------(1)
And the school took in $44 on the second day by selling 2 adult tickets and 6 child tickets, so the second equation is.
---------------(2)
We find the price of an adult ticket and the price of a child ticket by solving above system of equation.
Now, equation 2 multiplied by 7.
![7(2x+6y=44)](https://tex.z-dn.net/?f=7%282x%2B6y%3D44%29)
---------(3)
Now, equation 1 subtracted by equation 3.
![14x+42y=308](https://tex.z-dn.net/?f=14x%2B42y%3D308)
![14x+14y=224](https://tex.z-dn.net/?f=14x%2B14y%3D224)
-______________
14x is cancelled in both equations, so we get the equation.
![28y=84](https://tex.z-dn.net/?f=28y%3D84)
![y=\frac{84}{28}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B84%7D%7B28%7D)
y = 3
Now, we substitute y = 3 in equation 2.
![2x+6(3)=44](https://tex.z-dn.net/?f=2x%2B6%283%29%3D44)
![2x+18=44](https://tex.z-dn.net/?f=2x%2B18%3D44)
![2x=44-18](https://tex.z-dn.net/?f=2x%3D44-18)
![2x=26](https://tex.z-dn.net/?f=2x%3D26)
![x=\frac{26}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B26%7D%7B2%7D)
x = 13
Therefore, the price of the adult ticket is $13 and the price of the child ticket is $3.