Tickets for a basketball game cost $20 for upper-level seats and $30 for lower-level seats. tickets at the same venue for an ice hockey game cost $15 for upper-level seats and $35 for lower-level seats. if tickets for all seats are sold, the venue generates $7000 in revenue for a basketball game and $6500 for a hockey game. how many upper and lower-level seats does the venue have?

let x represent the number of upper-level seats.

let y represent the number of lower-level seats.

20x + 30y = 7000
15x + 35y = 6500

the venue has
upper-level seats and lower-level seats.

x = 200

y = 100

Step-by-step explanation:

20x + 30y = 7000       Divide by 10

15x + 35y = 6500       Divide by 5

It helps if you break down both equations to something simpler. It looks like not always.

(2x + 3y = 700)              Multiply by 3            

(3x + 7y = 1300)             Multiply by 2

6x + 9y = 2100

6x + 14y =2600              Subtract

-5y = - 500                     Divide by -5

-5y/-5 = -500/-5

y = 100

2x + 3y = 700                  substitute y = 100

2x+ 3*100 = 700              Combine

2x + 300 = 700                 Subtract 300 from both sides.

2x = 700 - 300

2x = 400

x = 400/2

x = 200

Hockey check

15x + 35y = 6500

15*200 + 35*100 = 6500

3000 + 3500 = 6500      Just as it should.  

step-by-step explanation:

de-gf

hj=3x+20

ji=15x-64