Diane is a manager at a small movie theater. On Wednesday, she sold twenty adult and children’s tickets. Adult tickets are $3 each. Children’s tickets are $2 each. On Wednesday, the theater made $125 from ticket sales. How many adult tickets were sold? How many children’s tickets were sold?
3*20<125; you sold more then 20 tickets or didn't make $125
To find the number of adult tickets sold, let's assume "x" to represent the number of adult tickets sold.
Since adult tickets are priced at $3, the revenue generated from adult ticket sales can be calculated by multiplying the number of adult tickets sold by the price of each adult ticket:
Revenue from adult ticket sales = x adult tickets * $3 per adult ticket
Similarly, let's assume "y" to represent the number of children's tickets sold.
Since children's tickets are priced at $2, the revenue generated from children's ticket sales can be calculated by multiplying the number of children's tickets sold by the price of each children's ticket:
Revenue from children's ticket sales = y children's tickets * $2 per children's ticket
We also know that the total revenue from ticket sales on Wednesday was $125. So, we can express this mathematically as:
Total revenue = Revenue from adult ticket sales + Revenue from children's ticket sales
Or,
$125 = x adult tickets * $3 per adult ticket + y children's tickets * $2 per children's ticket
Now, we can solve this system of equations to find the values of x and y. The solution will give us the number of adult and children's tickets sold.
Alternatively, since we know that there were a total of twenty tickets sold (adult + children), we can use this information to set up another equation:
Total tickets sold = Number of adult tickets + Number of children's tickets
Or,
20 = x adult tickets + y children's tickets
Now, we have a system of two equations:
$125 = x * $3 + y * $2
20 = x + y
We can solve this system of equations using various methods such as substitution or elimination to find the values of x and y.