Answer: the cost of an adult ticket is $8
the cost of a child ticket is $5
Step-by-step explanation:
Let x represent the cost of an adult ticket.
Let y represent the cost of a child ticket.
On the first day of ticket sales, the school sold 4 adult tickets and 7 child tickets for a total of $67.This means that
4x + 7y = 67 - - - - - - - - - -1
The school took in $106 on the second day by selling 12 adult tickets and 2 child tickets. This means that
12x + 2y = 106 - - - - - - - - - -2
Multiplying equation 1 by 12 and equation 2 by 4, it becomes
48x + 84y = 804
48x + 8y = 424
Subtracting
76y = 380
y = 380/76 = 5
Substituting y = 5 into equation 1, it becomes
4x + 7×5 = 67
4x + 35 = 67
4x = 67 - 35 = 32
x = 32/4 = 8
