The best estimate for the price of the discounted ticket is about $11.12, which corresponds to option the option (D)
(D) $11.15
The steps used to find the best estimate for the price of the discounted tickets can be presented as follows;
Let x represent the price of the standard tickets, and let y represent the price of the discounted tickets, we get;
Number of standard tickets = 153
Number of discounted tickets = 47
The total amount of tickets sales = $2,649.34
153·x + 47·y = 2,649.34
y = (2,649.34 - 153·x)/47
The best estimate for the price of the ticket, x can be obtained by finding the solution to the system of equation, which is the point of intersection of the graph of the first and second equations, that can be obtained where the x- and y-values of both equations are the same, that is we get;
y-value for the first equation, y = (2,649.34 - 153·x)/47 is equivalent to the y-value of the second equation, y = 0.80·x
Therefore; (2,649.34 - 153·x)/47 = 0.8·x
2,649.34 - 153·x = 47 × 0.8·x
2,649.34 = 47 × 0.8·x + 153·x
47 × 0.8·x + 153·x = 2,649.34
190.6·x = 2,649.34
x = 2,649.34/190.6
x = 13.9
The price of the standard ticket, x = $13.9
The price of the discounted ticket is therefore; y is; 0.8 × $13.9 = $11.12
Price of the discounted ticket is about $11.12. The best correct option therefore is option (D) $11.15