Concert tickets word problem

Question

Full price tickets for a concert cost $56.50. Students can purchase tickets at a discounted price for $49.50. If a total of 3250 tickets are sold and if the total amount of tickets sales was $162,611, how many full price tickets were sold and how many student tickets were sold. 

Answer 1

56.5r + 49.5d = 162611 

 

r + d = 3250

 

where r is the number of regular priced tickets and d is the number of discount tickets 

 

plugging in r = 3250 - d   Into the first equation:

 

183625 - 56.5d + 49.5d = 162611

 

-7d = 162611 - 183625 = -21014

 

d = 3002

 

plugging into the second equation above:

 

r = 248