SOLUTION: Adult tickets for the championship game are usually $5, but on Seniors' Day, seniors paid $4. Children's tickets were $2.50. Sales of 1,800 tickets totaled $7,425, and children and

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Adult tickets for the championship game are usually $5, but on Seniors' Day, seniors paid $4. Children's tickets were $2.50. Sales of 1,800 tickets totaled $7,425, and children and      Log On


   

Question 577694: Adult tickets for the championship game are usually $5, but on Seniors' Day, seniors paid $4. Children's tickets were $2.50. Sales of 1,800 tickets totaled $7,425, and children and seniors accounted for one-half of the tickets sold. How many of each ticket was sold?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = number of adult tickets sold
Let c = number of children's tickets sold
Let s = number of senior's tickets sold
given:
(1) +a+%2B+c+%2B+s+=+1800+
(2) +5a+%2B+2.5c+%2B+4s+=+7425+
(3) +c+%2B+s+=+900+
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Subtract (3) from (1)
(1) +a+%2B+c+%2B+s+=+1800+
(3) +-c+-+s+=+-900+
+a+=+900+
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and
(3) +c+%2B+s+=+900+
(3) +c+=+900+-+s+
----------------
Substitute into (2)
(2) +5a+%2B+2.5c+%2B+4s+=+7425+
(2) +5%2A900+%2B+2.5%2A%28+900+-+s+%29+%2B+4s+=+7425+
(2) +4500+%2B+2250+-+2.5s+%2B+4s+=+7425+
(2) +1.5s+=+7425+-+4500+-+2250+
(2) +1.5s+=+675+
(2) +s+=+675%2F1.5+
(2) +s+=+450+
and, since
(3) +c+=+900+-+s+
(3) +c+=+900+-+450+
(3) +c+=+450+
900 adult tickets were sold
450 children's tickets were sold
450 senior's tickets were sold