Final answer:
To determine the prices of a senior citizen ticket and a child ticket, we set up two equations from the sales data of two days and solved them using the elimination method. We found that the price of a senior citizen ticket is $14 and the price of a child ticket is $9.
Step-by-step explanation:
The question involves setting up a system of linear equations to solve for the price of a senior citizen ticket and a child ticket. We have two equations based on two days of ticket sales. On the first day, 2 senior tickets (S) and 2 child tickets (C) were sold for a total of $46, which can be represented as:
2S + 2C = 46
On the second day, 6 senior tickets and 5 child tickets were sold for a total of $129:
6S + 5C = 129
To find the price of a senior citizen ticket (S) and a child ticket (C), we will solve this system of equations. We can use either substitution or elimination methods. In this case, we can first simplify the first equation by dividing everything by 2:
S + C = 23
Then, we can multiply the simplified equation by 6 to eliminate the variable S from the second equation:
6S + 6C = 138
Now, we subtract the second given equation from this:
(6S + 6C) - (6S + 5C) = 138 - 129
C = 9
Now that we know the price of a child ticket is $9, we can substitute that into the simplified first equation:
S + 9 = 23
S = 23 - 9
S = $14
So, the price of a senior citizen ticket is $14, and the price of a child ticket is $9.