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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 $\$50$ each and general admission tickets sold for $\$34$ each. If $1520$ tickets were sold for a total of $\$64000$ , which of the following systems could be used to find the number of reserved tickets, $r$ , and the number of general admission tickets, $g$ , that were sold?

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Q. A concert venue sold two types of tickets for an upcoming concert: reserved tickets and general admission tickets. Reserved tickets sold for

\$50

each and general admission tickets sold for

\$34

each. If

1520

tickets were sold for a total of

\$64000

, which of the following systems could be used to find the number of reserved tickets,

r

, and the number of general admission tickets,

g

, that were sold?

Equations Setup: Let's denote the number of reserved tickets sold as $r$ and the number of general admission tickets sold as $g$ . 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.
Total Tickets Sold: The total number of tickets sold is $1520$ . This gives us our first equation: $\newline$ $r + g = 1520$ $\newline$ This equation represents the sum of reserved tickets ( $r$ ) and general admission tickets ( $g$ ) sold.
Total Revenue Calculation: The total revenue from ticket sales is $\$64000$ . Reserved tickets are sold at $\$50$ each, and general admission tickets are sold at $\$34$ each. This gives us our second equation: $\newline$ $50r + 34g = 64000$ $\newline$ This equation represents the total revenue generated from $r$ reserved tickets and $g$ general admission tickets.
Solving the System: Now we have a system of two equations with two variables: $\newline$ $1$ ) $r + g = 1520$ $\newline$ $2$ ) $50r + 34g = 64000$ $\newline$ This system can be used to find the values of $r$ and $g$ , which are the number of reserved and general admission tickets sold, respectively.

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