Tickets to a local performance sold for $3.00 for adults and $1.50 for children. If 170 tickets were sold for a total of $480 dollars, how many adult and children tickets were sold?
a + c = 170
3 a + 1.5 c = 480
a = 170 - c
3 (170 - c) + 1.5 c = 480
510 - 3 c + 1.5 c = 480
30 = 1.5 c
c = 20
then a = 150
To solve this problem, we can use a system of equations. Let's assume that the number of adult tickets sold is represented by the variable 'A', and the number of children tickets sold is represented by the variable 'C'.
According to the given information, the price of an adult ticket is $3.00, so the total revenue from adult tickets can be calculated by multiplying the price by the number of adult tickets sold: 3A.
Similarly, the price of a child ticket is $1.50, so the total revenue from children tickets can be calculated by multiplying the price by the number of children tickets sold: 1.5C.
We are also given that the total revenue from all the tickets sold is $480. So, we can write the equation: 3A + 1.5C = 480.
We are also given that the total number of tickets sold is 170. So, we can write another equation: A + C = 170.
Now, we have two equations:
3A + 1.5C = 480 -----(1)
A + C = 170 -----(2)
We can use these two equations to solve for A and C.
One way to solve this system of equations is by substitution.
Firstly, we can solve equation (2) for A: A = 170 - C.
Now, substitute the value of A in equation (1):
3(170 - C) + 1.5C = 480.
Simplifying this equation gives us:
510 - 3C + 1.5C = 480.
Combine like terms:
-1.5C = -30.
Divide both sides by -1.5:
C = 20.
Substitute the value of C back into equation (2) to find A:
A + 20 = 170,
A = 150.
Therefore, 150 adult tickets and 20 children tickets were sold.