Using a system of equations, the price of an adult ticket (A) is $3, and the price of a student ticket (S) is $12.
How to apply the system of equations?
Let A be the price of an adult ticket and S be the price of a student ticket.
On the first day, the school sold 14 adult tickets and 2 student tickets for a total of $66. This can be represented by the equation:
14A + 2S = 66
On the second day, the school sold 9 adult tickets and 13 student tickets for a total of $183. This can be represented by the equation:
9A + 13S = 183
Now, you have a system of two equations with two unknowns:
14A + 2S = 66
9A + 13S = 183
Use the elimination method here to solve:
Multiply the first equation by 13 and the second equation by 2 to make the coefficients of S the same:
182A + 26S = 858
18A + 26S = 366
Now subtract the second equation from the first to eliminate S:
(182A + 26S) - (18A + 26S) = 858 - 366
Simplify:
164A = 492
Divide by 164:
A = 3
Now that we know A = 3, substitute this back into one of the original equations:
14(3) + 2S = 66
42 + 2S = 66
Subtract 42 from both sides:
2S = 24
Divide by 2:
S = 12
So, the price of an adult ticket (A) is $3, and the price of a student ticket (S) is $12.