Children and adult tickets were sold for a local play. The children and adult tickets sold for $11 and $16, respectively. If 150 tickets were sold, and the total revenue was $2250 for the night, find the number of children and adult tickets sold.
add up the head-count, and the revenue:
c+a = 150
11c+16a = 2250
Now just solve for c and a.
To solve this problem, we can set up a system of linear equations using the given information.
Let's assume that the number of children's tickets sold is represented by 'c', and the number of adult tickets sold is represented by 'a'.
According to the problem, the total number of tickets sold is 150, so we can write the first equation as:
c + a = 150 ---> equation (1)
The second equation is based on the total revenue generated from the ticket sales. The revenue from children's tickets is $11 per ticket, and the revenue from adult tickets is $16 per ticket. So, we can write the equation as:
11c + 16a = 2250 ---> equation (2)
Now we need to solve this system of equations using any method such as substitution, elimination, or matrix. Let's solve it using the substitution method.
From equation (1), we have c = 150 - a.
Substituting this value of c into equation (2), we get:
11(150 - a) + 16a = 2250
Simplifying the equation, we get:
1650 - 11a + 16a = 2250
5a = 600
a = 120
Now substitute this value of a back into equation (1), we get:
c + 120 = 150
c = 30
Therefore, the number of children's tickets sold (c) is 30, and the number of adult tickets sold (a) is 120.