SOLUTION: a museum charges $5 for admission tickets, but members receive a 1$ discount and students are admitted for half price. one Saturday, 1050 tickets were sold for a total of $4035. if

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Question 1009657: a museum charges $5 for admission tickets, but members receive a 1$ discount and students are admitted for half price. one Saturday, 1050 tickets were sold for a total of $4035. if 35 more students' tickets than full price tickets were sold, find number of each type of tickets sold.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = number of admission tickets sold
Let +b+ = number of member tickets sold
Let +c+ = number of student tickets sold
-------------------------------------
(1) +a+%2B+b+%2B+c+=+1050+
(2) +5a+%2B+4b+%2B+2.5c+=+4035+
(3) +c+=+a+%2B+35+
---------------------------
Multiply both sides of (1) by +4+ and
subtract (2) from (1)
(1) +4a+%2B+4b+%2B+4c+=+4200+
(2) +-5a+-+4b+-+2.5c+=+-4035+
-----------------------------
+-a+%2B+1.5c+=+165+
+-2a+%2B+3c+=+330+
Substitute (3) into this result
+-2a+%2B+3%2A%28+a+%2B+35+%29+=+330+
+-2a+%2B+3a+%2B+105+=+330+
+a+=+225+
and
(3) +c+=+a+%2B+35+
(3) +c+=+225+%2B+35+
(3) +c+=+260+
and
(1) +a+%2B+b+%2B+c+=+1050+
(1) +225+%2B+b+%2B+260+=+1050+
(1) +b+%2B+485+=+1050+
(1) +b+=+565+
------------------
225 admission tickets were sold
565 member tickets were sold
260 student tickets were sold
----------------------------
check:
(2) +5a+%2B+4b+%2B+2.5c+=+4035+
(2) +5%2A225+%2B+4%2A565+%2B+2.5%2A260+=+4035+
(2) +1125+%2B+2260+%2B+650+=+4035+
(2) +4035+=+4035+
OK