Tickets for a show were available at the full price of $22 if purchased at the door but at a discount price of $15 if bought in advance. $6,860 was collected through the sale of 420 tickets. How many tickets sold were full-price tickets and how many were discount tickets?

Show how to solve this problem algebraically. Show work for this problem by defining variable(s), writing appropriate equation(s), and showing the solving process. Write a sentence to answer the question.

Question

Tickets for a show were available at the full price of $22 if purchased at the door but at a discount price of $15 if bought in advance.  $6,860 was collected through the sale of 420 tickets. How many tickets sold were full-price tickets and how many were discount tickets? 

Show how to solve this problem algebraically. Show work for this problem by defining variable(s), writing appropriate equation(s), and showing the solving process. Write a sentence to answer the question.

anonymous · Answer

let f=full price tickets
let d=discounted tickets

total of 420 tickets sold so

f+d=420

for a total price of $6860

22f+15d=6860

now solve 
f+d=420
22f+15d=6860
as a system of equations

anonymous · Answer

Thanks so much! I could not figure this problem out.