Final answer:
To find the price of the senior citizen and student tickets, set up a system of equations from the given information and solve using substitution or elimination. The price of a senior citizen ticket is found to be $1.17 and the price of a student ticket is $12.12.
Step-by-step explanation:
Nicole's school is selling tickets to a fall musical and we need to calculate the price of a senior citizen ticket and a student ticket based on the sales over two days. We can set up a system of equations to solve this problem using the given information. Let's denote the price of a senior citizen ticket as x and the price of a student ticket as y.
From the first day: 4x + 11y = $138
From the second day: 8x + 2y = $76
By using a method such as substitution or elimination, we can solve for x and y to find the ticket prices. For example, if we multiply the second equation by 2, we get:
16x + 4y = $152
Now we can subtract the first equation from this new equation to eliminate y:
12x = $14
x = $14 / 12
x = $1.17 (price of a senior citizen ticket)
Now, using the value of x in either the first or second original equation, we can solve for y:
4(1.17) + 11y = $138
4.68 + 11y = $138
11y = $138 - 4.68
11y = $133.32
y = $133.32 / 11
y = $12.12 (price of a student ticket)