SOLUTION: A total of 450 theater tickets were sold. Student tickets sold for $3 and adult tickets sold for $5. If total receipts were $2000, how many of each kind were sold?

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: A total of 450 theater tickets were sold. Student tickets sold for $3 and adult tickets sold for $5. If total receipts were $2000, how many of each kind were sold?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



Question 237454: A total of 450 theater tickets were sold. Student tickets sold for $3 and adult tickets sold for $5. If total receipts were $2000, how many of each kind were sold?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = number of student tickets sold
Let b = number of adult tickets sold
given:
(1) a+%2B+b+=+450
(2) 3a+%2B+5b+=+2000
Multiply both sides of (1) by 3 and
subtract (1) from (2)
(2) 3a+%2B+5b+=+2000
(1) -3a+-3b+=+1350
2b+=+650
b+=+325
and, since
(1) a+%2B+b+=+450
(1) a+%2B+325+=+450
a+=+450+-+325
a+=+125
125 student tickets and 325 adult tickets were sold
check:
(2) 3a+%2B+5b+=+2000
(2) 3%2A125+%2B+5%2A325+=+2000
375+%2B+1625+=+2000
2000+=+2000
OK