A student sells tickets to a school play . Adults ticket cost $8 each , and children tickets cost $5 each. The student sells a total of 12 tickets and collects a total of $72 from the ticket sales. How many adults tickets does the student sell?
number of adults -- x
number of chidren -- 12-x
solve for x
8x + 5(12-x)=72
Let's assume the student sells "a" adult tickets and "c" child tickets.
According to the given information, the total number of tickets sold is 12, so we can write this as an equation:
a + c = 12 ...........(1)
The total amount collected from the ticket sales is $72. Since adult tickets cost $8 each and child tickets cost $5 each, we can write another equation for the total amount collected:
8a + 5c = 72 ...........(2)
Now, we can solve these two equations to find the values of "a" and "c".
We can start by multiplying equation (1) by 5:
5a + 5c = 60 ...........(3)
Now, subtract equation (3) from equation (2) to eliminate "c":
8a + 5c - (5a + 5c) = 72 - 60
8a - 5a = 12
3a = 12
a = 12/3
a = 4
So, the student sold 4 adult tickets.
To solve this problem, we can use a system of equations.
Let's say the student sells "x" number of adults tickets and "y" number of children tickets.
From the given information, we know that the total number of tickets sold is 12. Therefore, we can write the equation:
x + y = 12 --> Equation 1
We also know that the total amount collected from ticket sales is $72. The cost of each adult ticket is $8, and the cost of each children ticket is $5. So, the total amount collected can be expressed as:
8x + 5y = 72 --> Equation 2
Now, we have a system of two equations (Equation 1 and Equation 2). We can solve this system to find the values of "x" and "y," which represent the number of adult and children tickets, respectively.
One way to solve this system is by substitution.
From Equation 1, we can express "y" in terms of "x" as:
y = 12 - x
Substituting this value of "y" into Equation 2, we get:
8x + 5(12 - x) = 72
Now, solve this equation:
8x + 60 - 5x = 72
3x + 60 = 72
3x = 12
x = 4
So, the student sells 4 adult tickets.
To find the number of children tickets, substitute the value of "x" into Equation 1:
4 + y = 12
y = 12 - 4
y = 8
Therefore, the student sells 4 adult tickets and 8 children tickets.