Tickets to a local movie store were sold at $3.00 for adults and $1.50 for students. If 170 tickets were sold for a total of $480.00, how many adult tickets were sold?
just add up the value of all the tickets sold.
3.00a + 1.50(170-a) = 480.00
a = 150
To solve this problem, we can set up a system of equations based on the given information. Let's say the number of adult tickets sold is "a" and the number of student tickets sold is "s".
From the problem statement, we know that the total number of tickets sold was 170:
a + s = 170 (Equation 1)
We also know that the total revenue from ticket sales was $480. Since adult tickets cost $3.00 and student tickets cost $1.50, the total revenue can be expressed as:
3a + 1.5s = 480 (Equation 2)
Now we have a system of two equations (Equation 1 and Equation 2) that we can solve simultaneously to find the values of "a" and "s".
There are several methods to solve a system of equations, such as substitution, elimination, or using matrices. Let's use the method of substitution:
1. Solve Equation 1 for one variable in terms of the other variable. We can solve for "a":
a = 170 - s
2. Substitute this expression for "a" into Equation 2:
3(170 - s) + 1.5s = 480
3. Distribute 3 through the parentheses:
510 - 3s + 1.5s = 480
4. Combine like terms:
-1.5s = -30
5. Divide both sides by -1.5 to solve for "s":
s = 20
Now we know that 20 student tickets were sold. We can substitute this value into Equation 1 to find the number of adult tickets:
a + 20 = 170
a = 150
Therefore, 150 adult tickets were sold.