A total of 326 adult and students tickets were sold for a high school play. The ticket prices were $8 for adults and $5 for students. If a total of $1972 was collected from ticket sales, how many student tickets were sold
Let x be the number of adult tickets sold.
Then the number of student tickets sold is 326 - x.
The total revenue from adult tickets is 8x.
The total revenue from student tickets is 5(326 - x).
The total revenue is 1972.
So 8x + 5(326 - x) = 1972.
So 8x + 1630 - 5x = 1972.
So 3x + 1630 = 1972.
So 3x = 342.
So x = 114.
The number of student tickets sold is 326 - 114 = <<326-114=212>>212. Answer: \boxed{212}.
To find the number of student tickets sold, we can set up a system of equations.
Let's say the number of adult tickets sold is x, and the number of student tickets sold is y.
According to the problem, the total number of tickets sold is 326, so we can write the equation:
x + y = 326 (Equation 1)
The price of an adult ticket is $8, and the price of a student ticket is $5. The total amount collected from ticket sales is $1972, so we can write another equation:
8x + 5y = 1972 (Equation 2)
Now we have a system of equations that we can solve to find the values of x and y.
To solve this system of equations, we can use the substitution method or the elimination method.
Let's use the substitution method:
From Equation 1, we can express x in terms of y:
x = 326 - y
Substituting this value of x into Equation 2, we get:
8(326 - y) + 5y = 1972
Now we can solve for y:
2608 - 8y + 5y = 1972
-3y = -636
y = -636 / -3
y = 212
So, 212 student tickets were sold.
Let's assume the number of adult tickets sold be 'A' and the number of student tickets sold be 'S'.
We are given:
A + S = 326 (Equation 1) (There were a total of 326 tickets sold)
8A + 5S = 1972 (Equation 2) (The total amount collected from ticket sales was $1972)
To solve the equations, we can use the method of substitution or elimination.
Let's solve using the substitution method.
From Equation 1, we can express A in terms of S by rearranging the equation as A = 326 - S.
Now we substitute this value of A in Equation 2:
8(326 - S) + 5S = 1972
Simplifying the equation:
2608 - 8S + 5S = 1972
Combine like terms:
-3S = 1972 - 2608
-3S = -636
Divide both sides by -3:
S = -636 / -3
S = 212
Therefore, 212 student tickets were sold for the high school play.