Question

1. a movie theater sold 100 tickets for a show. adult tickets cost $12 each and student tickets cost $8 each. if the total sales were $980, how many adult tickets and how many student tickets were sold? let x = tickets, y = money (100x + 8y = 980) 500x + 50 = 980

Explanation:

Step1: Define variables

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

Step2: Set up ticket count equation

$x + y = 100$

Step3: Set up sales total equation

$12x + 8y = 980$

Step4: Isolate $y$ from Step2

$y = 100 - x$

Step5: Substitute $y$ into Step3 equation

$12x + 8(100 - x) = 980$

Step6: Simplify and solve for $x$

$12x + 800 - 8x = 980$
$4x = 180$
$x = \frac{180}{4} = 45$

Step7: Solve for $y$ using $x=45$

$y = 100 - 45 = 55$

Answer:

45 adult tickets and 55 student tickets were sold.