Question

1. exactly 185 tickets were sold for an orchestra concert. the total amount collected in ticket sales was $1,600. advance tickets, ( a ), cost $8 each and tickets sold at the door, ( d ), cost $10 each. write and solve a system of equations algebraically to determine the number of advanced and door tickets were sold.

Explanation:

Step1: Define variables & total tickets

Let $a$ = number of advance tickets, $d$ = number of door tickets.
$a + d = 185$

Step2: Define total sales equation

$8a + 10d = 1600$

Step3: Isolate $a$ from Step1

$a = 185 - d$

Step4: Substitute into sales equation

$8(185 - d) + 10d = 1600$
$1480 - 8d + 10d = 1600$
$1480 + 2d = 1600$

Step5: Solve for $d$

$2d = 1600 - 1480$
$2d = 120$
$d = 60$

Step6: Solve for $a$

$a = 185 - 60$
$a = 125$

Answer:

125 advance tickets and 60 door tickets were sold.