Question

Hey 1200 seat theater sells two types of tickets for a concert. premium seats sell for $30 each and regular seats so for $20 each at one event $30,180 was collected and ticket sales with 10 seats left on so how many for each type of ticket was sold

Answer 1

Answer:

Number of premium tickets sold = 638      

Number of regular tickets sold = 552

Step-by-step explanation:

Let number of premium tickets sold be p and number of regular tickets be r.

Total number of seats = 1200

Ticket sales with 10 seats left on, that is

               p + r = 1190     ----------------eqn 1

Cost of premium ticket = 30 $

Cost of regular ticket = 20 $

Money collected = 30180 $

Total money collected = 30 p + 20 r = 30180

                       3p + 2 r = 3018     ----------------eqn 2

eqn 1 x 2

               2p + 2r = 2380 --------------------eqn 3

eqn 2 - eqn 3

                  p = 3018 - 2380 = 638

Substituting in eqn 1

                638 + r = 1190  

                 r = 552

Number of premium tickets sold = 638      

Number of regular tickets sold = 552

Answer 2

X = premium seats
y = regular seats
You need two equations: (x + y - 10 = 1200) and (30x + 20y = 30,180)
1.) Isolate one variable
y = 1,210 - x
2.) Plug the new equation into the second ORIGINAL equation
30x +20(1,210 - x) = 30,180
3.) Ditribute
30x + 24,200 - 20x = 30,180
4.) Add like terms
10x + 24,200 = 30,180
5.) Subtract 24,000 from either side
10x = 6,180
6.) Solve for x
x = 618
7.) Plug in x to the equation of your choosing
618 + y - 10 = 1200
8.) Solve for y
608 + y = 1,200
y = 592
The theater sold 592 regular seats and 618 premium seats.