Question

scenario: a theater sold 102 tickets for a total revenue of $1,932. adult tickets were $21 and student tickets were $15. how many of each were sold? hint define your variables and set up your equations and use desmos graphing calculator to find the solution. screenshot the graph and paste here. solution: solution:

Explanation:

Step1: Define variables

Let $x$ = number of adult tickets, $y$ = number of student tickets.

Step2: Set up total tickets equation

Total tickets sold: $x + y = 102$

Step3: Set up total revenue equation

Total revenue: $21x + 15y = 1932$

Step4: Isolate $y$ from Step2

$y = 102 - x$

Step5: Substitute $y$ into revenue equation

$21x + 15(102 - x) = 1932$

Step6: Simplify and solve for $x$

$21x + 1530 - 15x = 1932$
$6x = 1932 - 1530$
$6x = 402$
$x = \frac{402}{6} = 67$

Step7: Solve for $y$ using $x=67$

$y = 102 - 67 = 35$

Answer:

67 adult tickets and 35 student tickets were sold.