Q:

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 = 700015x + 35y = 6500The venue hasupper-level seats and lower-level seats.

Accepted Solution

A:
Answer:x = 200y = 100Step-by-step explanation:20x + 30y = 7000       Divide by 1015x + 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 = 21006x + 14y =2600              Subtract-5y = - 500                     Divide by -5-5y/-5 = -500/-5y = 1002x + 3y = 700                  substitute y = 1002x+ 3*100 = 700              Combine2x + 300 = 700                 Subtract 300 from both sides.2x = 700 - 3002x = 400x = 400/2x = 200===================Hockey check15x + 35y = 650015*200 + 35*100 = 65003000 + 3500 = 6500      Just as it should.