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

f = full price tickets
d = discount tickets

f + d = 420 --> f = 420 - d
22f + 15d = 6860
now sub 420 - d in for f in the second equation
22f + 15d = 6860
22(420 - d) + 15d = 6860
9240 - 22d + 15d = 6860
9240 - 7d = 6860
-7d = 6860 - 9240
-7d = - 2380
d = -2380/-7
d = 340
now sub 340 in for d
f + d = 420
f + 340 = 420
f = 420 - 340
f = 80
check...
22f + 15d = 6860
22(80) + 15(340) = 6860
1760 + 5100 = 6860
6860 = 6860 (correct)
ANSWER: Full price tickets (f) sold were 80
              Discount tickets (d) sold were 340
For a total of (80 + 340) 420 tickets sold at (1760 + 5100) $ 6860.