Adult tickets for the school play cost 5 dollars and students cost $3. Thirty more students tickets were sold then adult tickets. If $1762 was collected, how many of each type of ticket was sold?
3x+5y+3(30)=1770
x=y
3x+5x=1680
x=210
210 adult
240 student
To solve this problem, we can use a system of equations to represent the given information. Let's define two variables:
Let's call the number of adult tickets sold as 'x' and the number of student tickets sold as 'y'.
According to the first piece of information, adult tickets cost $5, so the total revenue from adult tickets would be 5x dollars.
Similarly, the revenue from student tickets can be calculated by multiplying the cost of each ticket ($3) by the number of student tickets sold, which is 'y'. So, the total revenue from student tickets would be 3y dollars.
The second piece of information states that thirty more student tickets were sold than adult tickets. So, the equation representing this relationship would be y = x + 30.
Lastly, the total revenue collected from all the tickets is given as $1762. We can write this as an equation as well: 5x + 3y = 1762.
Now, we have a system of equations:
Equation 1: y = x + 30
Equation 2: 5x + 3y = 1762
We can solve this system of equations to find the values of 'x' and 'y' (the number of adult tickets and student tickets respectively).