Saturday night the movie theater sold 60 student tickets and 20 adult tickets earning $450. Sunday afternoon the movie theater sold 20 student tickets and 32 adult tickets earning $340. How much does a student tickets and an adult ticket cost?
Let S stand for student price and A for adult price.
60S + 20A = 450
20S + 32A = 340
Multiply second equation by 3.
60S + 96A = 1020
Subtract first equation from revised second.
76A = 570
A = $7.50
Insert value into first equation to find S.
To find out the cost of student tickets and adult tickets, we can use a system of equations. Let's assume that the cost of a student ticket is "S" dollars and the cost of an adult ticket is "A" dollars.
From the given information, we can set up the following equations:
Equation 1: 60S + 20A = 450 (representing the Saturday night sales)
Equation 2: 20S + 32A = 340 (representing the Sunday afternoon sales)
Now we have a system of equations with two unknowns. We can solve this system using various methods, such as substitution or elimination.
One way to solve it is by using the substitution method. We'll start by solving Equation 1 for S:
60S + 20A = 450
=> 60S = 450 - 20A
=> S = (450 - 20A) / 60
Now substitute this value of S into Equation 2:
20((450 - 20A) / 60) + 32A = 340
=> (6000 - 400A) / 60 + 32A = 340
=> 100 - 6.67A + 32A = 340
=> 25.33A = 240
=> A ≈ 9.48
So the approximate cost of an adult ticket is $9.48.
Now, substitute this value of A back into Equation 1:
60S + 20(9.48) = 450
=> 60S + 189.6 = 450
=> 60S = 450 - 189.6
=> 60S = 260.4
=> S ≈ 4.34
So the approximate cost of a student ticket is $4.34.
Therefore, a student ticket costs approximately $4.34 and an adult ticket costs approximately $9.48.