Final answer:
The price of a senior citizen ticket is $6 and the price of a child ticket is also $6.
Step-by-step explanation:
To find the price of a senior citizen ticket and the price of a child ticket, we can set up a system of equations based on the information given. Let's use the variables 's' for the price of a senior citizen ticket and 'c' for the price of a child ticket.
On the first day, we know that 7 senior citizen tickets and 12 child tickets were sold for a total of $114. This can be represented by the equation 7s + 12c = 114.
On the second day, 14 senior citizen tickets and 13 child tickets were sold for a total of $162. We can represent this with the equation 14s + 13c = 162.
Now we can solve this system of equations to find the values of 's' and 'c'.
Using the elimination method, we can multiply the first equation by -2 and add it to the second equation to eliminate 's'. This gives us the new equation -14s - 24c = -228 + 14s + 13c = 162. Simplifying, we get -11c = -66. Solving for 'c', we find that c = 6.
Substituting this value of 'c' into the first equation, we can solve for 's'. 7s + 12(6) = 114. Simplifying, we get 7s + 72 = 114, and by subtracting 72 from both sides, we find that 7s = 42. Solving for 's', we get s = 6.
Therefore, the price of a senior citizen ticket is $6, and the price of a child ticket is also $6.