Tickets to a local movie were sold at $4.00 for adults and $2.50 for students. If 173 tickets were sold for a total price of $642.50, how many student tickets were sold?

Question

Tickets to a local movie were sold at $4.00 for adults and $2.50 for students.  If 173 tickets were sold for a total price of $642.50, how many student tickets were sold?

Isaiah Anthony · Accepted Answer

#33# student tickets were sold.

If #173# tickets were of adult total collection would be of #173*4.00= $692.00# Difference of collection #(692.00-642.50) = $49.50# is due to student concession of #(4-2.50)=$1.50 # per ticket. Therefore number of student tickets were #49.50/1.50=33# [Ans]

Ethan Adkins · Answer

undefined Let's denote the number of adult tickets sold as $ A $ and the number of student tickets sold as $ S $.

We know that the total number of tickets sold is 173:

$ A + S = 173 $  (1)

We also know that the total revenue from the sale of tickets is $642.50:

$ 4A + 2.50S = 642.50 $  (2)

Now, we can solve this system of equations. Let's first multiply equation (1) by 4 to eliminate the fractions:

$ 4A + 4S = 692 $  (3)

Now, subtract equation (3) from equation (2) to eliminate $ A $:

$ 4A + 2.50S - (4A + 4S) = 642.50 - 692 $

$ -1.50S = -49.50 $

Divide both sides by -1.50:

$ S = \frac{-49.50}{-1.50} $

$ S = 33 $

Therefore, 33 student tickets were sold.