The school that Cody goes to is selling tickets to the annual dance competition. On the first day of ticket sales the school sold 13 adult tickets and 8 child tickets for a total of $108. The school took in $106 on the second day by selling 2 adult tickets and 14 child tickets. Find the price of an adult ticket and the price of a child ticket.
To find the price of an adult ticket and the price of a child ticket, we can set up a system of equations based on the given information.
Let's assume the price of an adult ticket is A and the price of a child ticket is C.
On the first day, the school sold 13 adult tickets and 8 child tickets for a total of $108. This can be expressed as:
13A + 8C = 108 --Equation 1
On the second day, the school sold 2 adult tickets and 14 child tickets for a total of $106. This can be expressed as:
2A + 14C = 106 --Equation 2
Now, we have a system of equations:
13A + 8C = 108 --Equation 1
2A + 14C = 106 --Equation 2
To solve this system of equations, we can use the method of substitution or elimination.
Let's solve it using the method of substitution:
1. Rearrange Equation 1 to express A in terms of C:
13A = 108 - 8C
A = (108 - 8C)/13
2. Substitute the value of A in Equation 2:
2((108 - 8C)/13) + 14C = 106
3. Simplify and solve for C:
216 - 16C + 182C = 1378
166C = 1162
C = 7
Now, we have the value of C, which is the price of a child ticket.
4. Substitute the value of C in Equation 1 to find A:
13A + 8(7) = 108
13A + 56 = 108
13A = 52
A = 4
Therefore, the price of an adult ticket is $4 and the price of a child ticket is $7.
a= adult ticket
c=child ticket
13a+8c=108
2a+14c=106
use elimination to solve for a and c