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

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1 week 2021-07-21T05:24:32+00:00 1 Answers 0 views 0

1. x = the number of $3 tickets y = the number of$5 tickets

z = the number of $6 tickets the group sells$3, $5, and$6 tickets, and receives exactly $503 from the sale of tickets 3x + 5y + 6z = 503 the number of$5 tickets is twice the number of $6 tickets y = 2z the number of$3 tickets is 1 more than 3 times the number of \$6 tickets

x = 1 + 3z

by solving the system of equations

3x + 5y + 6z = 503

y = 2z

x = 1 + 3z

we find

x = 61 tickets

y = 40 tickets

z = 20 tickets