Final answer:
Roberta sold 30 tickets in total, with 10 adult tickets and 20 student tickets. The cost of a student ticket was $3. Ken collected $200 in total and sold 20 student tickets.
Step-by-step explanation:
To solve this problem, we can set up two equations based on the given information. Let's use variables to represent the unknown quantities.
Let's say the cost of an adult ticket is A dollars. Then the cost of a student ticket would be 3/4 of A dollars, or (3/4)A dollars.
Based on the information given, we can set up the following equations:
Robera sold 10 more student tickets than adult tickets, so let's say she sold X adult tickets and X + 10 student tickets.
The total collected by Roberta was $212.50, so we have the equation:
(A * X) + ((3/4)A * (X + 10)) = $212.50
Ken sold 50 tickets in total, so he sold 50 - (X + 10) student tickets. The total collected by Ken was $200, so we have the equation:
((3/4)A * (50 - (X + 10))) + (A * X) = $200
Now we can solve these equations to find the values of X and A.
Plugging in A = 4, we get X = 10. Therefore, Roberta sold 10 adult tickets and 20 student tickets. The cost of a student ticket was (3/4) * 4 = $3.
In conclusion, Roberta sold 30 tickets in total, with 10 adult tickets and 20 student tickets. The cost of a student ticket was $3. Ken collected $200 in total and sold 20 student tickets.