Final answer:
To find the price of a senior citizen ticket, set up a system of equations using the given information and solve for the variables. The price of a senior citizen ticket is $12.
Step-by-step explanation:
To find the price of a senior citizen ticket, we will set up a system of equations using the given information. Let's assume the price of a senior citizen ticket is $x and the price of a child ticket is $y.
From the information on the first day of ticket sales, we can set up the equation:
2x + 3y = 51
From the information on the second day of ticket sales, we can set up the equation:
8x + 13y = 213
We can solve this system of equations using the method of substitution or elimination to find the values of x and y. Once we find the value of x, we will know the price of a senior citizen ticket.
Using the elimination method, we can multiply the first equation by 8 and the second equation by 2 to eliminate the variable y:
16x + 24y = 408
16x + 26y = 426
Subtracting the first equation from the second equation, we get:
2y = 18
y = 9
Substituting the value of y back into the first equation, we can solve for x:
2x + 3(9) = 51
2x + 27 = 51
2x = 24
x = 12
Therefore, the price of a senior citizen ticket is $12. So the correct answer is option d) $10.