SOLUTION: Tickets to a local movie were sold at $5.00 for adults and $3.50 for students. If 370 tickets were sold for a total of $1415.00, how many adult tickets were sold?

Question 432960: Tickets to a local movie were sold at $5.00 for adults and $3.50 for students. If 370 tickets were sold for a total of $1415.00, how many adult tickets were sold?
Found 2 solutions by mananth, Lstark01:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Adult tickets number x cost
child tickets numbers ------------ y cost
x+y=370 .............1
5x+3.5y =1415 .............2
Eliminate y
multiply (1)by -3.5
Multiply (2) by 1
-3.5x-3.5y=-1295
5x+3.5y=1415
Add the two equations
1.5x=120
/1.5
x=80 Adult tickets numbers

Answer by Lstark01(4) (Show Source): You can put this solution on YOUR website!
your 2 equations to solve this are:
A + C = 370
5.00A + 3.50C = 1415.00
In the first equation, if you subtract C from both sides you get:
A = 370 - C
substitute this in for the second equation.
5.00(370-C) + 3.50C = 1415.00
1850 - 5.00C + 3.50C = 1415.00
1850 - 1.5C = 1415.00
-1850 on both sides
-1.5C = -435.00
Divide by -1.5 on both sides
C = 290 children tickets.
Then:
A + 290 = 370
Subtract 290 from both sides
A = 80 adult tickets were sold.
If you want to check your work:
5.00(80) + 3.50(290) = 1415.00
400.00 + 1015 = 1415.00
1415.00 = 1415.00
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