Question

a concert manager counted 350 ticket receipts the day after a concert. the price for a student ticket was $12.50, and the price for an adult ticket was $16.00. the register confirms that $5,075 was taken in. how many student tickets and adult tickets were sold?

select one:
a. 150 student tickets and 200 adult tickets.
b. 120 student tickets and 220 adult tickets.
c. 160 student tickets and 190 adult tickets.
d. 180 student tickets and 170 adult tickets.

Explanation:

Step1: Define variables

Let $s$ = number of student tickets, $a$ = number of adult tickets.

Step2: Set up total tickets equation

Total tickets: $s + a = 350$ → $s = 350 - a$

Step3: Set up total revenue equation

Total revenue: $12.50s + 16.00a = 5075$

Step4: Substitute $s$ into revenue equation

Substitute $s=350-a$:
$12.50(350 - a) + 16.00a = 5075$

Step5: Expand and simplify

$4375 - 12.50a + 16.00a = 5075$
$3.50a = 5075 - 4375$
$3.50a = 700$

Step6: Solve for $a$

$a = \frac{700}{3.50} = 200$

Step7: Solve for $s$

$s = 350 - 200 = 150$

Answer:

A. 150 student tickets and 200 adult tickets.