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A concert venue sold two types of tickets for an upcoming concert: reserved tickets and general admission tickets. Reserved tickets sold for $50\$50 each and general admission tickets sold for $34\$34 each. If 15201520 tickets were sold for a total of $64000\$64000, which of the following systems could be used to find the number of reserved tickets, rr, and the number of general admission tickets, gg, that were sold?

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Full solution

Q. A concert venue sold two types of tickets for an upcoming concert: reserved tickets and general admission tickets. Reserved tickets sold for $50\$50 each and general admission tickets sold for $34\$34 each. If 15201520 tickets were sold for a total of $64000\$64000, which of the following systems could be used to find the number of reserved tickets, rr, and the number of general admission tickets, gg, that were sold?
  1. Equations Setup: Let's denote the number of reserved tickets sold as rr and the number of general admission tickets sold as gg. We are given two pieces of information: the total number of tickets sold and the total revenue from ticket sales. The first equation will represent the total number of tickets sold, and the second equation will represent the total revenue.
  2. Total Tickets Sold: The total number of tickets sold is 15201520. This gives us our first equation:\newliner+g=1520r + g = 1520\newlineThis equation represents the sum of reserved tickets (rr) and general admission tickets (gg) sold.
  3. Total Revenue Calculation: The total revenue from ticket sales is $64000\$64000. Reserved tickets are sold at $50\$50 each, and general admission tickets are sold at $34\$34 each. This gives us our second equation:\newline50r+34g=6400050r + 34g = 64000\newlineThis equation represents the total revenue generated from rr reserved tickets and gg general admission tickets.
  4. Solving the System: Now we have a system of two equations with two variables:\newline11) r+g=1520r + g = 1520\newline22) 50r+34g=6400050r + 34g = 64000\newlineThis system can be used to find the values of rr and gg, which are the number of reserved and general admission tickets sold, respectively.

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