SOLUTION: I cannot figure out how to get how many tickets were sold for each priced ticket. A basketball team sells tickets that cost $10, $20, or, for VIP seats, $30. The team has sold

Algebra ->  Finance -> SOLUTION: I cannot figure out how to get how many tickets were sold for each priced ticket. A basketball team sells tickets that cost $10, $20, or, for VIP seats, $30. The team has sold      Log On


   

Question 1077610: I cannot figure out how to get how many tickets were sold for each priced ticket.
A basketball team sells tickets that cost $10, $20, or, for VIP seats, $30. The team has sold 3343 tickets overall. It has sold 113 more $20 tickets than $10 tickets. The total sales for $62,350. How many tickets have been sold?
How many $10 tickets were sold?
How many $20 tickets were sold?
How many $30 tickets were sold?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x, how many $10 tickets
y, how many $20 tickets
z, how many $30 VIP tickets

Follow the description.
system%28x%2By%2Bz=3343%2Cy-x=113%2C10x%2B20y%2B30z=62350%29

Three linear equations in three unknown variables, so solve the system.
You would want to simplify the sales equation to x%2B2y%2B3z=6235, and the second equation maybe as -x%2By=113.

Work with THIS system:
system%28x%2By%2Bz=3343%2C-x%2By=113%2Cx%2B2y%2B3z=6235%29


One path to begin can be, add first and second equations to form a new equation; and add the second and third equations to form another new equation. This eliminates x, and your two new equations are in just the two variables, y and z.