Let's use the variable, x, represent the price of an adult ticket and the variable, y, represent the price of a student ticket.
We can write the following equations to represent the two days sales amounts:
6x + 7y = $74
2x + 14y = 118
Now we can solve these two equations with two unknowns to find the price of each type of ticket.
Multiply the first equation by -2 to find the price of the adult ticket first:
6x + 7y = $74 becomes -12x - 14y = -148
Now combine this "new" equation with the second one:
-12x - 14y = -148
2x + 14y = 118
-10x = -30
x = $3
The cost of one adult ticket is $3.
Now substitute $3 for x in either of the original equations to find the price y of one adult ticket (Let's use the first equation.)
6x + 7y = 74
6 • 3 + 7y = 74
18 + 7y =74
18 + 7y - 18 = 74 - 18
7y = 56
y = $8
The price of a child ticket is $8 also.
