. A total of 326 adult and student 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?
To solve this problem, we can set up a system of equations using the given information.
Let's assume that the number of adult tickets sold is "a" and the number of student tickets sold is "s".
We know that the total number of tickets sold is 326, so we have the equation:
a + s = 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. We can use this information to create another equation:
8a + 5s = 1972 -- Equation 2
We now have a system of two equations (Equation 1 and Equation 2) with two variables (a and s). We can solve this system to find the values of a and s.
There are different ways to solve this system, but one common method is called substitution:
1. Solve Equation 1 for a:
a = 326 - s
2. Substitute the value of a from Step 1 into Equation 2:
8(326 - s) + 5s = 1972
3. Simplify and solve for s:
2608 - 8s + 5s = 1972
-3s = 1972 - 2608
-3s = -636
s = -636 / -3
s = 212
Therefore, 212 student tickets were sold.
a+s = 328
8a+5s = 1972