Answer:
the price of an adult ticket is $8, and the price of a child ticket is $14.
Explanation:
To find the price of an adult ticket and the price of a child ticket, we need to set up a system of equations. Let "A" represent the price of an adult ticket and "C" represent the price of a child ticket.
On the first day, the school sold 3 adult tickets and 1 child ticket for a total of $38, so we can set up the following equation to represent this information:
3A + C = 38
On the second day, the school took in $104 by selling 6 adult tickets and 4 child tickets, so we can set up the following equation to represent this information:
6A + 4C = 104
Now that we have our two equations, we can solve for the values of A and C. We can use the elimination method to solve this system of equations. To do this, we need to multiply one of the equations by a constant so that one of the variables has the same coefficient in both equations. We'll multiply the first equation by 2:
6A + 2C = 76
We can then subtract this equation from the second equation to eliminate the C term:
6A + 4C - 6A - 2C = 104 - 76
This simplifies to:
0A + 2C = 28
Dividing both sides by 2, we get:
C = 14
We can now substitute this value for C in one of our original equations and solve for A. We'll use the first equation:
3A + 14 = 38
Subtracting 14 from both sides, we get:
3A = 24
Dividing both sides by 3, we get:
A = 8
Therefore, the price of an adult ticket is $8, and the price of a child ticket is $14.