## An amateur theater group is converting a large classroom into an auditorium for a forthcoming play. The group will sell $3, $5, and $6

An amateur theater group is converting a large classroom into an auditorium for a

forthcoming play. The group will sell $3, $5, and $6 tickets. They want to receive

exactly $503 from the sale of the tickets. If the number of $5 tickets to be sold is twice

the number of $6 tickets, and the number of $3 tickets is 1 more than 3 times the

number of $6 tickets, how many $3 tickets are there?

## Answers ( )

x = the number of $3 ticketsy = the number of $5 ticketsz = the number of $6 ticketsthe group sells $3, $5, and $6 tickets, and receives exactly $503 from the sale of tickets3x + 5y + 6z = 503the number of $5 tickets is twice the number of $6 ticketsy = 2zthe number of $3 tickets is 1 more than 3 times the number of $6 ticketsx = 1 + 3zby solving the system of equations3x + 5y + 6z = 503y = 2zx = 1 + 3zwe findx = 61 ticketsy = 40 ticketsz = 20 tickets