Roberta sold fifty tickets for the school play. Roberta sold ten more student tickets than adult tickets. How many student tickets did Roberta sell?
From this result, if the total cost of a student ticket was three-fourths the cost of an adult ticket, and Roberta collected a total of 212.50, what was the total cost of a student ticket?
30x+20y=212.50
x=3/4y
20(3/4y)+20y=212.5
Go from there, and when you solve for y, put that back in the original equation at the top for x.
what does x stand for and what does y stand for?
x=student tickets, y=adult tickets
okay.. but...20(3/4y)+20y=212.5 ... when u solve this we get a decimal... and is this equation to find the COST of a student ticket...
To find out how many student tickets Roberta sold, we need to solve the first part of the problem.
Let's assume the number of adult tickets sold as 'x'. According to the given information, Roberta sold ten more student tickets than adult tickets. So, the number of student tickets sold can be represented as 'x + 10'.
Now, we know that the total number of tickets sold is 50. Therefore, we can set up the equation: x + (x + 10) = 50.
Simplifying the equation, we get: 2x + 10 = 50.
Subtracting 10 from both sides of the equation, we have: 2x = 40.
Dividing both sides by 2, we get: x = 20.
So, Roberta sold 20 adult tickets. Now, we can find out the number of student tickets sold:
x + 10 = 20 + 10 = 30.
Therefore, Roberta sold 30 student tickets.
Moving on to the second part of the problem, we need to calculate the cost of a student ticket.
Let's assume the cost of an adult ticket as 'y'. According to the given information, the total cost collected by Roberta was 212.50.
We know that Roberta sold 20 adult tickets, so the cost of the adult tickets sold is 20y. Since the cost of a student ticket is three-fourths the cost of an adult ticket, the cost of a student ticket is (3/4)y.
The total cost collected can be represented as the sum of the cost collected from adult tickets and the cost collected from student tickets:
20y + 30 * (3/4)y = 212.50.
Simplifying the equation, we have: (20y + 22.5y) = 212.50.
Adding the coefficients of 'y', we get: 42.5y = 212.50.
Dividing both sides by 42.5, we have: y = 212.50 / 42.5.
Thus, y = 5.
So, the cost of an adult ticket is $5. Since the cost of a student ticket is three-fourths of the cost of an adult ticket, the cost of a student ticket is (3/4) * 5 = $3.75.
Therefore, the total cost of a student ticket is $3.75.