Andrea’s school is selling tickets to the fall musical. On the first day of ticket sales, the school sold 3 adult tickets and 11 child tickets for a total of $82. The school took in $114 on the second day by selling 6 adult tickets and 12 child tickets. What is the price of one adult ticket and one child ticket?

One adult ticket is $9 and one child's ticket is $5

Step-by-step explanation:

let a = adult tickets

let c = child tickets

3a + 11c = 82

6a + 12c = 114

multiply the first equation by -12 and the second by 11 to eliminate c

-12(3a + 11c = 82)

11(6a + 12c = 114)

-36a - 132c = -984

66a + 132c = 1254

add both equations

30a = 270

30       30

a = 9

plug in the value of a into any equation to find the value of c

3a + 11c = 82

3(9) + 11c = 82

27 + 11c = 82

-27             -27

11c = 55

11       11

c = 5

plug in the value to check if it's right

6a + 12c = 114

6(9) + 12(5) = 114

54 + 60 = 114

hope this helps