Emily's school is selling tickets to the annual talent show.

On the first day of ticket sales, the school sold 11 senior citizen tickets and 4 student tickets for a total of $133.

The school took in $182 on the second day by selling 10 senior citizen tickets and 8 student tickets.

Find the price of a senior citizen ticket and the price of a student ticket.

a) Senior citizen ticket: $9, Student ticket: $8
b) Senior citizen ticket: $8, Student ticket: $9
c) Senior citizen ticket: $11, Student ticket: $4
d) Senior citizen ticket: $4, Student ticket: $11

To determine the price of senior citizen and student tickets, let's define the price of a senior citizen ticket as s and the price of a student ticket as t.

We are given two equations based on the ticket sales:

11s + 4t = 133 (first day sales)
10s + 8t = 182 (second day sales)

By multiplying the first equation by 2, we get:

22s + 8t = 266

Now, we can subtract the second day's equation from this to eliminate t:

22s + 8t - (10s + 8t) = 266 - 182
12s = 84

Dividing both sides by 12, we get s = 7. To find t, substitute s into one of the original equations:

11(7) + 4t = 133
77 + 4t = 133
4t = 56
t = 14

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