SOLUTION: A theater has tickets at $6 for adults, $3.50 for students, and $2.50 for children. A total of 278 tickets were sold with a total revenue of $1300. If the number of adult tickets

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A theater has tickets at $6 for adults, $3.50 for students, and $2.50 for children. A total of 278 tickets were sold with a total revenue of $1300. If the number of adult tickets       Log On


   

Question 894770: A theater has tickets at $6 for adults, $3.50 for students, and $2.50 for children. A total of 278 tickets were sold with a total revenue of $1300. If the number of adult tickets sold was 10 less than twice the number of students tickets, how many of each ticket were sold for the showing?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
g = how many adult tickets
s = how many student tickets
c = children tickets


g%2Bs%2Bc=278 and g=-10%2B2s;
-10%2B2s%2Bs%2Bc=278
highlight_green%283s%2Bc=288%29, accounts for tickets but g is eliminated.

6g%2B3.5s%2B2.5c=1300 starting with account of revenue.
6%282s-10%29%2B3.5s%2B2.5c=1300
12s-60%2B3.5s%2B2.5c=1300
15.5s%2B2.5c=1360
highlight_green%2831s%2B5c=2720%29, accounts the revenue, also g is eliminated.

Start equation solution as elimination, using 5 times the ticket count equation:
31s%2B5c-%2815s%2B5c%29=2720-5%2A288
16s=1280
highlight%28highlight%28s=80%29%29


You take care of the rest of the solution for g and c.